Other than that, I couldn't agree more. It is astonishing how much more business friendly about anything is in the US vs EU. Although, it's easily forgotten, that in the US you still often deal with certain local taxes/regulations that sometimes somewhat remind someone of the EU :)
No that's not how it works.
A corporation is a legal person operating from the place where it's incorporated and ruled by the law in the place where it's incorporated. The western world (and plenty of countries outside it) has laws and/or trade agreements that allow foreign corporations to operate within their borders in a (not so) limited way. It's true that in some (many) cases it's necessary to create a local subsidiary for the US corporation, but it's not triggered just by the founder/shareholder (much less a CEO) sitting/working from there. Usually - and especially in the EU-US case - even having employees there is _not_ enough to necessitate a local subsidiary, but it makes everything about it very much easier.
The only way to move money from a corporation to shareholders (excluding cases where a shareholder is also an employee) is via dividends. These dividends are your personal income and thus taxed by the rules of your tax residence (that's a technical term in EU and outside) - the usual rule is "where you sit for half of the calendar year plus one day". Ask your local tax authority about it and they will hand out a guide, owning foreign corporations is a very normal arrangement.
An alternative to dividends is keeping the money inside the corporation and selling your stake. Again, that's your personal income - you are the owner and you sold it to another person - and it's taxed by the rules for this kind of income where your tax residence is.
Might be different with a LLC, though. This is a C Corp.
