Why don't they stay? European countries have an incredibly high rate of approval of their healthcare. It's still my opinion that healthcare here is only the best in the world if you're wealthy. If it sucked over there they wouldn't have so many happy people. There are always anecdotes, but according to the stats they are doing great.
They don't move because their old friends, kids and grandkids are over there. They do complain a lot about conditions there though.
And, I'm not talking mere anecdotes; I'm talking real people with firsthand knowledge.