The scenario that you describe is exactly what happened to my Dad. He moved to Florida in the early 70's with his second wife. By the mid 80's he was diagnosed with cancer and endured multiple surgeries until it took him in 1991. All of his children lived here in Maryland and had jobs and children to care for. It gets expensive traveling that far frequently especially when you have a family to take care of.
I still have my siblings and extended family here in Maryland. I guess I'll be staying but I'm not liking what I see coming down the pike.
I told my mom just yesterday that if she gets infirm and needs someone to take care of her she has to come to FL because I'm not living in NE with those absurd winters. She got all mehmehmeh and I said fine, I'll just wait until I can declare you incompetent and move you down anyway.
My grandparents and great-grandparents never had kids taking care of them - they died in their own home before it got to that point. I expect my folks will do that as well, and I hope I do too.