I have an immigrant family on my street (know them and they are from China) that is three generations...every morning as I drive to work I pass the grandparents walking the children to the bus stop for school. Every day I think "why don't our parents live with us"? I've asked them but they've said no. They have their own home and lives and like their independence. Maybe that's true, but I wonder if they're actually lonely and don't want to impose. At the end of the day I just have to think this is a mutually non-beneficial setup for all involved (the US style of moving out "never to return" at 18).
I don't pretend to know why or say how to "fix" it but I believe we in the U.S. (and assuming at least some of the "west") took a wrong path somewhere when it comes to this.
Also constantly see in the media examples of college grads living and working from home, always in a "negative" economic-driven context. Maybe this is a trend that is changing (again in my opinion for the better).
I didn't even bring up nursing homes.
Edit: Constant ""'s are because I'm trying to be aware of over-generalize here...mainly speaking for "mainstream U.S. culture" which is always problematically reductive