If the 'foreign entrepreneur' is rich then he or she does not need VC help to immigrate into the United States. I know a few - it just requires being able to get in via O visa, which is easy for a rich person[1]. So this means that the foreign entrepreneur in question is not rich.
A non-rich foreign entrepreneur is unlikely to have the kind of salary that allows one to throw money at the problem to make inconveniences of switching countries go away:
1. Establishing personal credit, bank accounts, dealing with financial institutions, insurance etc
2. Getting state issued drivers license and dealing with Government
3. Getting an apartment
4. Developing a quick understanding of good v. bad areas, social norms (poor person with terrible habits is an asshole. Rich person with the same habits is eccentric ), etc
[1] Edit: In a response to the comment below - lets define "rich" as someone with a few million in assets with a million of that being liquid.