Whether ironing is pointless depends on the clothes. There’s no point in dironing jeans, but dress shirts are another
But to answer your question, I’ll say a video game console. Utterly useless and frankly quite boring. 
We got five picnic baskets. Married 21 years and have never been on a picnic. I do use one for magazines.
Replaced the blower motor on ours last week. Wore it out after 11 years.
We have like three of these. Use them only to for a traditional picnic effect. Last time maybe 15 years ago. We may have ditched them since, I haven’t looked. If one exists, it is on the pantry shelf next to the punch bowl set. Bowl works as a holiday candy bowl, but the cups are useless.
This is why registries are such a great thing. You can pick things they want, and get a feel for what they DON’T want.
When my parents were married in 1962, they got about 10 dozen wine glasses. Most were returned or regifted :D, and I have never seen either of them use a wine glass.
I’m going to second spamforbrains central vacuum suggestion (post #100). Like PoppaSan (#103) I too own a central vac system, use it for all my vacuum needs and I think it does a superior job.
But the setup time makes quick or short vacuum jobs problematic. I think if I were to move and the new abode had a central vac system I would probably never use it.
BTW, I bet less than 2% of homes in the U.S. have a central vac system so such a system does not fit into the criteria of the OP.
Along with bibles and phone books, I’ll add dictionaries to the list of books that aren’t used very often.
I know! It’s that little (still sealed) package of four round rubber feet that came with your old router, portable phone base, or clock/radio. It’s in the kitchen, in the junk drawer next to the silverware drawer, way at the back.
And some people have little soaps, shampoos and lotions brought home from hotels. Also never used.
We use our laundry chute virtually every day. Saves us having to schlep things down from the second floor to the basement . . . when and if we’re going down to the basement.
And this house also has a phone nook in the dining room. I still keep a classic rotary phone in it, sort of as a museum/conversation piece.
And how many people have fireplaces in their homes but never use them? I have two, and would use them more often if I weren’t concerned with smoke affecting all the art work on the walls.
My parents used it all the time, and infrequently used it until it broke in half, and I never had a chance to replace it. I use the flat side a lot more than the bumpy side (Love schnitzels and thinly pounded chicken breast), but it got good use.
We use dictionaries a lot. I know people who use their Bibles a lot. Not at all comparable to phone books. They’re not as commonplace and are used much more.
I use them, or donate them to the food pantry if they’re unopened.
I had one of those. Took me YEARS to figure out that it turned on the lights in the detached garage.
I nominate just about any decorative thing that a woman buys for the bedroom, especially those frilly little dresses that you put around the bed. Being a guy, what I require is a place to lay my weary head. Frills, duvets, bed dresses, throw cushions, stuffed teddy bears, etc. are all, to put it kindly, optional – just as optional as those decorative little soap thingies in the bathroom that no one would ever dare use. Why is it that women consider a bed unfit for habitation unless it’s wearing at least 537 different items of apparel like an Edwardian Prince of Wales?
I find it awesome for making refried beans from dried beans. It’s almost the only thing I ever use it for - somehow potatoes are rarely eaten in mashed form around here. Well, I guess sometimes I mash squash or other vegetables, like parsnips.
Perfect for smashed potatoes!
And here I thought the modern cooler (for the needs-kept-cold stuff) and the reusable canvas bag (for the not-cold stuff) obsoleted picnic baskets a long time ago…
This is insane. You are insane! There is nothing wrong with buying a few things to make your life easier, and you can pry my toaster oven from my cold dead hands.
I know and I like the whipped ones better.
Not all women, please! I don’t have any of that stuff in my bedroom, or the decorative soap. The only thing I will argue with you on is the “frilly dress” for the bed. The purpose for that is to hide whatever’s under your bed. This way those under the bed bins, the lady’s vibrator, or just a bin of sexy, sexy things, can be hidden. Or anything else. That’s all it’s for. 
I doubt anywhere near 90% of households have a Bible. And a lot of people who do have one read it sometimes. In many cases that might be done online rather than with the physical book, but then it’s really the same category as reference books (encyclopedia, dictionary, phone book) whose function has tended to be taken over by computers. But IME that’s less completely true of Bibles than say phone books.