The funny thing is that not that many people that would be able to afford this would actually do it. The USA is a nice country but there are many parameters that go in to the decision of choosing a place to live and it scores low on plenty of those. The US is the destination country of choice for people without money. Those with money are just as likely to go elsewhere.
I have to disagree, at least anecdotally. I know several people, whom I'm pretty sure don't have to work if they don't want to. Yet they moved to the US specifically in order to start companies. And even they, rich, educated folk from "good" countries have had ridiculous amounts of trouble getting visas and work permission.
But anecdotes are nice, numbers are better. For every wealthy person that would like to get 'in' to the US there must be 50,000 poor ones.
The difference is that for them nobody is going out of their way to create special visa to allow them entrance.