I’d also say (as several others have already mentioned): Even if you feel you could win a battle of attrition with your kid, unless you know from experience that that battle will be quiet and unnoticeable to people around you, please don’t choose a nice restaurant, where other people are trying to enjoy a meal in a nice setting, as your battlefield.
Neurologically, childrens’ taste palettes are also developing from infanthood where they naturally desire things that are sweet and fatty, and many just lack the complexity to appreciate savory, bitter, or complex spiced dishes. Children are also really much more sensitive to the texture and temperature of foods than adults.
I find it somewhat hilarious that this complaint is coming from the guy who considers White Castle ‘burgers’ to be good food..
Stranger
Sorry, I just re-read this. Plain white rice isn’t much better for you than grilled cheese - in fact, Grilled cheese at least has protein ( Kraft Singles American cheese slices contain 4 grams of protein per slice) and honestly is not very palatable as a stand alone.
And sauteed broccoli? Lots of luck with sliding that past a young kid.
distributes obligatory bunch of belt onions
As has been said many times, it’s much easier to let your child order something that they’ll definitely like and try to get them to sample something interesting you ordered, than to force parents into forcing their kids to order/eat from the main menu. When my kids were little, the oldest ordered off the kids menu until she was like 16, the middle one started off the real menu by the time she was 8, and the youngest had a bunch of allergies so often wound up with (very good) special-order chicken fingers. I fail to see how that affected other diners.
Don’t forget why don’t authentic Mexican restaurants serve queso dip?
On a cruise, though, the specialty restaurants have access to the main dining room and its freezer.
Keep dino shaped cookie cutters in your go-bag. Any restaurant will have an item that can be cut into a dino shape. Chicken Katsu → instant dino nuggets.
As an “other diner,” I’d much prefer to have a happy kid at the next table and not have to hear a power struggle over the sushi mom wants the little one to try.
Well exactly. Our kids ate what they wanted and no one heard a power struggle. The “other diner” I was referring to is the OP whose dining experience is apparently lessened by seeing the words “chicken fingers” on the children’s menu.
My comment perhaps made it appear that I was disagreeing with you. I was not. We’re in agreement.
Surprisingly, one place that offers a more adventurous kid’s menu is Walt Disney World. Many of the table service restaurants offer steak or fish options for the little Mouseketeers.
Given that my experience of even pretty high-end establishments is that the children’s menu usually comes on a piece of paper covered with games and puzzles, I’m wondering how OP is exposed to it at all.
Give those crayons back to the kids!
Once your phone is out of juice so you can’t Dope while dining alone, a guy’s gotta do something to occupy his time. Doodling on the paper kids’ menu with the crayons can be a fine diversion. And you get something to hang on your fridge with your dino-shaped magnets. 
FTR: I am dining (well, lunching) alone and Doping on my tablet just now. No crayons; no kids menu.
But how accurate is their perception of the market? Is there circular reasoning going on that they only sell X, Y & Z on their menu then justify it saying people are ordering X, Y & Z?
Little chains and mom-and-pops, sure you might see such circular reasoning going on.
I’ve worked with several large, national casual-dining and fast-food chains during my career, and they have an entire pipeline system to come up with new ideas, which, yes, does include talking to customers (and potential customers) to learn what they might be interested in, doing surveys and focus groups, and conducting test markets of promising new ideas.
is their understanding perfect? Undoubtedly not. Are some chains missing some idea that could be huge for them? Maybe. But, they probably do have a pretty darned good view of what their customers actually want.
Given the relative difficulty of working up a new menu item for a national chain restaurant system versus whipping up a variation on an e-commerce site, I wonder how much A/B testing - Wikipedia goes on in that industry?
I think you misfiled this. The Extremely common in TV or movies but almost never happens in real life thread is down the hall. 
A/B testing is a very common technique in consumer market research. It isn’t appropriate for every research project, but I can assure you that the big chains use it, among a number of other research techniques.
For example, a chain might have a potential new recipe for an existing menu item: the new recipe might represent a cost savings, might use an ingredient from a different supplier, etc. They recognize that tinkering with the current recipe of a popular item has a big potential downside (i.e., angering loyal customers who like the current formulation), and so, they’d almost undoubtedly conduct one or more market research studies before making the switch across their chain.
Those research studies would likely include an A/B test among current customers who regularly eat that menu item, testing the current recipe (cell A) and the new recipe (cell B), to see if there are any significant differences in how customers experience and like the recipes.
My completely amateur and unscientific experience is that restaurants tend to open with larger menus and then pare back as some things prove unpopular or unprofitable. I wouldn’t be surprised if smaller/family restaurants tend to open with a slightly more extensive children’s menu then take off the kid’s meatloaf and kid’s chicken parm after it turns out that most of the kids are happy eating cheeseburgers and chicken nuggets.