Yes. Pre-railroad people mostly didn't move and inheriting furniture was extremely helpful. Go back earlier and the cost of buying your own furniture would have been prohibitive.
My parents are both 70+, they have 3 big cabinets from their parents, made from solid wood. I’d not mind having them in the right place. They look and handle great, only the drawers could use some finetuning ;)
A modern mattress won't fit on the old fame and will be more comfortable. If you replace the stuffing of the old mattress maybe it will be as good.
sighs.
I have tried new beds (granted, not as expensive ones) and they were worse than the 40 years old spring bed I have.
This somehow a point in your question, but I leave it to others to figure out what.
Grandpa donated the letters to the local historical society so they are accessible, though I'm not sure how.
And my wife inherited three pieces from her parents and they make up much of our dining room, and her uncle gave her two pieces that he made by hand, and that did not fit into his new house. I was dubious about the stuff from her parents, but it’s beautiful if dated and we’ve gone with a very “eclectic” decorating style, no room has to look like any other room. And now I’m very grateful for all of it.
My electric standing desk and chair being one of those modern things that costed a couple of thousands but i got secondhand for a combined 200. The desk is built like a tank. For the chair i replaced the cracking armrest covers with leather.
I also have some hardwood old tables and cabinets that are a couple generations old and as functional now as they were back then.
So yes, people do want to inherit the old stuff. I have some IKEA stuff (the beds were just too big, and mattress sizes are different), it just can't compare.
I'm going to challenge this assertion: did anyone, ever? Looking around in my parents' house (retirement age), there's no furniture from their parents (post-WW2). I don't remember whether my grandparents had any furniture of their parents in use either.
I do recall going to the charity shops and finding older wooden furniture; while I recognize it as better quality as what you can get today, at the same time it's no longer useful today. TV cabinets (with doors) for CRT TVs and video tapes, writing tables, those kinds of things are obsolete. Tables are timeless though.
But also, over time a lot of that old furniture was either destroyed or bought up and exported. What you find in the charity stores near me today is mostly 90's and onwards.