Well, I did not live in a home with a garbage disposer until I bought this house in 1997. It came with an 80's era Waste Kind SS5000, which apparently was already on its last legs (lots of jamming) and which I recently replaced with at 3/4 hp Titan. Prior to that, lived in a number of rental apts, flats, homes, none of which had disposers. Most didn't even have 220 service, for that matter. And none had a dishwasher. I remember renting a week of a vacation condo on Maui back in the 80's, and spending no little time trying to figure out how the dishwasher was supposed to work (there was no manual!).
Nowadays I would regard the essentiality of various kitchen appliances in this order, from most to least (assuming most kitchens already have stove, fridge, toaster, microwave, stand mixer, etc):
1) Clothes washer/dryer. OK, many of these live in laundry rooms or closets, but more than a few hang out under counters on on wheels in kitchens. And we all know how essential an automatic clothes washer is to civilized existence.
2) Dishwasher. I really dislike hand-washing large amounts of dishes. A few pots and pans, and large items, ok. But all that flatware... yeccch... rooting around the bottom of a slippery wash basin for them... yeeech.... and nothing seems to clean residual grease off as well as a good automatic dishwasher.
3) Garbage disposer. The ultimate solution for those icky dish drain strainers, which can be almost impossible to shake free of their loads, and once soiled never seem to get clean again. I still put a lot of food waste in the garbage, but for the stuff that remains in the sink the disposer is indispensable. I know I do miss not having a disposer in the patio kitchen sink... which means I have to dump wet waste into the garbage can there, which can be a problem since it doesn't get emptied as often as that in the main house kitchen.
4) Trash compacter. Never had one, but I could see how one might be useful. Current garbage collection service provides large green waste and recycling containers, so the regular can rarely gets filled up. But if the collection company actually enforced its ban on styrofoam in the recycling container, I'd seriously consider a compacter (assuming it would have the oomph to compact styrofoam blocks).
I'm sure we could add more to this list, but it's all I can think of at the moment.