Thucy is wrong on more than just the "what if there are no kids" standpoint.
This is not a nursing home - we're talking about places like America House -- these are very nice facilities. My grandmother moved to one when she got old, and it was perfect. It offered her independence when she wanted it, care when she wanted it. She had her own apartment - it was hers, just like any other apartment, except that the building also hd a cafeteria, a hot tub, nursing care, etc if she wanted to take advantage of them.
You ar assuming that every old person wants to give up their independence and move in with the kids. You - of course - are wrong. That is an option for some, not all.
In this case, you - as an old person - have to option of moving in to a facility with other people your age, with similar llikes, dislikes, etc.
Other problems with the Thucy solution -- what if the kids work, as many people work in to their 60's and even 70's...meaning they can't be there 24/7 to care for their elderly parents..
On a rather practical level - some families just don't get along that well to move in together...and that doesn't mean it's the kids fault. Some parents are assholes.
Hell, I think of this sort of otpion as college dormitory for old folks. I had a blast living in the dorms - my only responsibility was cleaning my own space and doing laundry. Frankly, I hope to god I can find a decent place to live with like-minded people when I'm old with a decent cafeteria if I want, etc and be able to shuffle down the hall and pound on old Draugnar's door if I want to get up a game.