Years ago, my then girlfriend was in sales, so she was on the road all week. When we decided to go out to eat, she would ask where I wanted to go. I’d say that anything is fine, letting her decide since she was on the road all week. One time she got mad at me, and told me to pick some place. From then on, I would offer the first choice. For the rest of our relationship, she never accepted my first choice. As a reply, she would tell me where she wanted to eat, and we would go there. Weirdly efficient.
At home with the kids, I handle it a little differently. We plan menus together, and I’m generally good with each kid putting something they like on the weekly dinner rotation (so we eat a lot of pan-fried dumplings and a lot of homemade fried rice). If I want to make something spicy, like a curry, I’ll cook them an alternative meal out of those ingredients (say, cauliflower and pan-fried chicken thighs and rice). Otherwise, their dinner choices are:
- Eat what we serve and have dessert.
- Grab a bowl of Cheerios and skip dessert.
- Complain, be responsible for getting their own dinner together, and skip dessert.
Option 1 and 2 are equally valid options, no judgment if they want to politely choose option 2.
Over time, they’ve slowly come to appreciate new foods.
Early on, we had a lot of conversations about how sometimes you eat food because it’s a delicious, pleasurable experience; and other times you eat food because your body needs fuel. It’s okay to say, “this food will be painful or traumatic for me to eat” and skip it; I do that sometimes too. (Arugula is the devil’s green). But if a food just doesn’t excite you? That’s cool, your body needs food, fuel it.
We use the OP’s method, with the caveat that if only 2 people are involved, I think it’s OK (indeed, beneficial) to omit the part about all vetoes being final. For example: “Burgers?” “No, Thai” “No…OK, I can get on board with burgers”.
When our kids are involved, it’s pretty much we pick the menu out of things we know they like, and they can either eat it or go hungry. It’s not normally an issue. Maybe not the best for trying new foods (though we will always give them the opportunity to try what we’re having, if it’s different from their meal) but it usually gets through mealtimes with decent nutrition and lower stress.
That’s pretty much my stance now.
“Do you have any preferences on what we eat tonight?”
“No.”
“Then this is what we are having.”
My better half and I used to have similar issues, but after trying to eat better, we pretty much stopped eating out except on vacation. The main exception is our favorite Thai place (because we both love it and have been going there for over 20 years) which is always a ‘yes’ to both of us.
As for cooking at home, it actually got easier when my wife decided to eat vegetarian. Partially because of the eating better, but mostly because she doesn’t like the taste and texture of meat. So we each cook for ourselves, but with coordination for some shared options. For example, if I’m making rice as a side or for fried rice, I’ll ask if she wants some anytime in the next 48 hours, and if so I’ll make extra.
If she’s making fried tofu (a weakness of hers), she’ll ask if I want to use the oil to fry anything after she’s done, so tempura shrimp or the like becomes a sudden option for me. Short version, being considerate to one’s spouse and being comfortable with different tastes goes a long way. The only real problem is that with pretty much dual cooking every day, I’m doing a load of dishes every day for just two people. 
for home meals, this is what we do. We try not to cook things someone else actually hates, but other than that, your night to cook, your choice, and your responsibility to come up with something.
We used to do that, in fact we actually raised him in the kitchen, teaching him how to use the stove and knives and stuff, then Great Gma happened. She was aghast that we let a 5 year old boil water and peel carrots and cut bread while we watched and supervised (we WATCHED and did nothing else while he was doing these things)
Sigh, I’d let him get his own food but he’d starve himself to death on cereal and cheesy chips
When my wife was recovering from retinal surgery and couldn’t drive we started menus. We shop Fridays because they have specials then. Thursday night we inventory the freezer, go through the cookbooks and recipe clippings, and decide on the menu for next week. That way we can put the ingredients on the grocery list. Saves money since we target our menus to what is on special, and saves lots of time. Really came in handy when we wanted to minimize our grocery store trips.
We seldom eat out (or get take in) so when we do picking one of a couple of places we like is easy, since we don’t go to any one place very often. We tend to pick things too complicated for us to cook at home in the sense of little bits of lots of ingredients.
We both can cook well and prefer our cooking to most local restaurants, good as they are.
We used to schedule the meals but now don’t, except for ones that have to work around 7 pm Zoom meetings.
IOW: Lead, follow, or expect to be run over. 
I’m happy in any of the 3 roles: leading, following, or running over. The counterparty(ies) just need to decide which they prefer: leading, following, or being run over. Whether that decision is by commission or omission, it’s still totally their decision.
I cook every day for the family. I sometimes will ask: “Is there anything in particular you want for dinner tonight?” when I’m being indecisive. If nobody gives me a suggestion, then I just make whatever I feel like, or whatever makes the most sense to use up food in our freezer and fridge (this makes my wife happy) with the caveat that it is something that I know everyone else will eat (or I’ll make a separate, simple dish for the young kids.)
But, for the most part, I’m just left to my own devices and they trust I’ll make something everyone will eat. I actually don’t usually ask for input. (In fact, my wife, as I was typing this post, asked “what’s for dinner today?” Creamy tarragon-lemon chicken soup and leftovers, if anyone is wondering.)
I make food and everyone has to eat it. No complaints.
Meat prices usually decide the options and I only vaguely plan 3-4 nights of the week. I also usually try and get a soup made.
So if a full pork loin is $1.69 a pound. That will decide the week. An 8 inch chunk will be a roast with potato’s and carrots. I’ll cut 6 steaks to have with a rice or noodles side. I’ll thinly slice and pound out the remainder for breaded cutlets or stir fry. Salad is an option for every meal and there will be at least one other veggie.
I fill the rest with leftovers (Sundays roast will be hash and gravy), breakfast for dinner, or Pillsbury pizza crust pizza (Friday night)
If the next week has a ham at $.96 a pound. We’re having boiled ham dinner, Cuban sandwiches, split pea soup, and ham and eggs.
A big hunk of beef will be sliced for cheessteaks, shredded for tacos or enchiladas, cut into a steaks or steak bites.
Yeah, BC, I used to cook based on what looked good in the supermarket. Peaches are on sale? That steak looks really good? Great, I know part of the menu.
Now I’m cooking from my freezer. 
Yeah, Covid (and the election) pushed me more towards the Cash and Carry style, restaurant supply stores. Hence the bulk meats and simpler menus. 50 lb boxes of boneless skinless chicken thighs. Entire beef bottom rounds made into london broils. Vacuum packed entire pork loins, or pork sirloin roasts. Build a soup off the leftovers.
It’s probably both a little practical and a little psychological.
A bowl of granola always works.
IMO, much of our obesity epidemic results from eating as a social exercise. People feel coerced into eating what, when, where and how their companion does.
When I became single, I lost 40 pounds
(from 5’11" / 185) in two years, and remained fit and healthy, just by taking full control of my diet.
Living only with my adult daughter, I just make what I want to eat, knowing what she likes. If I’m making something she doesn’t like, she can either make something very simple herself (she’s autistic) or she can cook a ready meal, or order something.
I really fucking hate the tyranny of deciding what to eat every night. It’s just food. A couple of nights a week, I might want to put effort in, the rest of the time, we have protein, veg and carbs and it gradually gets eaten.
Actual full cooked sit-down meals every day are not necessary.
My partner is a really good cook and always wants to try new dishes. But since just about everything she prepares is fantastic, my answer always is “What we had yesterday!”. And I never get it!
I do the shopping weekly. I also do all the cooking. We get our own breakfast - cereal or toast, and our own lunch - sandwich, soup, etc. I cook the evening meal, mostly from scratch.
On Thursday evening we make a list. Stock items like washing powder and tins of tomatoes go on First but then we try to create menus. Saturday is the big meal of the week, usually pork, beef, lamb or chicken - this meal always has leftovers. It may also be a stew, which means a supply of curries for the freezer or spag boll ditto. Sunday is always fish.
We may agree a couple of ideas for the other four meals, but it may also depend on what’s on offer.
During the week we often switch things around depending on how enthusiastic about cooking I feel. There are a couple of meals my wife likes that are a bit more trouble to make, so that’s a treat once a month or so.
There is always enough food in the fridge, freezer and cupboards to keep us going for quite a while.
We’re a lot less organized than you all. Or maybe just lazier. We do a weekly shop on Friday and one thing I always buy is a rotisserie chicken. It becomes two main meal’s (Saturday and Tuesday) worth of cooked chicken for whatever – tacos or stir fry or salads or chicken and rice type casseroles or whatever – plus on Thursday I cook up the carcass to make soup or stew. Oh, and Friday we always pick up take out something on the way home from the store.
So that’s four of the week’s meals ‘planned’, plus we generally have pasta on Wednesday and ‘breakfast’ type meal on Mondays (waffles and omelets and french toast and the like.)
That only leaves Sunday, and once a week one of us is generally able to come up with something that we’d actually like to eat. 
I used to play the “I dunno, what about you?” game all the time with a friend of mine who is even more accommodating and self-effacing than I am. And since I’m that way myself I knew exactly what was going on - both of us wanted the other person to be happy, and so would willingly go along with what the other wanted - and would refrain from making our own suggestion because we knew the other person would go along with it rather than suggesting what they actually wanted. Which is to say, we were each trying to figure what the other person wanted to do without ‘poisoning the well’ with our own desires.
After some months of this nonsense, I struck upon this strategy.
Step one - brainstorming: Each person has to suggest two or three options, in round robin fashion.
Step two - elimination: Each person has to eliminate one or more of the options, also in round robin.
Sometimes the elimination process gets the number of options down to one, in which case you’re done. If you get down to two or three options and the point where nobody wants to eliminate any of the remaining options, though, you then proceed to step three - consult a higher power. At that point we would defer the decision to The Great Decider - a six-sided dice.
The brainstorming step let us be confident we’d heard which option the other person actually wanted - though we couldn’t just assume that the first thing they suggested is their solid preference because perhaps they’d prefer what we suggested first, or perhaps they’re truly ambivalent that day. The elimination step helped us to start making the decision, because everyone is required to eliminate at least one and it doesn’t feel like you’re imposing your will if you’re just eliminating one option out of five - and once you’ve heard the other person eliminate an option you know that they’re expressing their will. And the Great Decider (hallowed be its name - ours was transparent green with white pips) allowed us to completely avoid the feeling that we had dictated the final option and enforced our will.
So once the Decider had Spoken, we’d all get ready to start doing what it had chosen. At which point step four would come into play - second thoughts. On rare occasions my friend would say, “you know, actually I’d rather do this instead.” At which point we would immediately switch to that, obviously. The process avoids the choice being something somebody else really wants (as far as anyone knows), so it’s easier for a self-effacing person to realize that once their actual preference has been snatched away by the Decider, that perhaps they really do want to do that thing after all.
I will add that I’m aware that this is all hugely complicated, but in the end it saves so much time, because the average running length for the “figure out what we’re going to do” game is half an hour or more.