Believe it or not but there are Americans who relinquish their passport precisely because of this reason. Patriotism is automatically assumed but we live in a globalised world.
Did you know that US has tools to claim part of your wealth even if you relinquishment the citizenship. Google "exit tax" for us citizens.
The US exit tax is a tax on your worldwide assets. The tax applies to all property that you own on the date of renunciation
That seems very likely, but I'd like the names of a few billionaires to verify.
The US is fairly unique in imposing an "expatriation" tax precisely to avoid this situation. The IRS taxes all of their assets as if sold on the day before expatriation.
Of course collecting taxes internationally is difficult, but anyone wealthy enough to meet the criteria will probably need to visit the US at some point.