Distance, as mentioned by choocotrekkie, is one thing. Most people like being near old friends and having their privacy.
Its the frail and elderly, perhaps with dehabilitating diseases that need specialist care. Your house might not have a suitable room for a parent or both downstairs, or a downstairs loo/ bathroom. Your parents may sell their house to pay for it, but its more likely they will refuse to imagine that scenario until its too late and they are in and out of hospital.
My dm, always said one benefit of being an orphan was she didn't have elderly parents. She took in her mil when none of mils children would. I had to give up my room and sleep in my parents on a camp bed. I had nowhere to do homework or hang out as a teen. Of course, my alcoholic df used to wake me up coming into the bedroom drunk and shouting. It disturbed granny, who hated my dm. And so on, for about 6 months before my dm said enough!
My dm refused to live with any of us. She refused a home as she wanted to be in her own house. She wasnt sociable and knew it. She didnt want us seeing her the way she was. That was her right. We respected it. It wasnt about us and how we felt.
My dc, well who knows where they will end up, or who with. I don't expect them to make life decisions based on my care when old.
The Asia model - how old are the stats they are looking at? Asians have embraced globalisation too, they might not be in a position to do that. No doubt active gp may live with them, but not when needing care, medical and otherwise round the clock.
All this assumes every old person has dc they like and like them back. Not always the case!