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US ignores the first $108k/year you make at the federal level as long as you spend 330/365 days out of country. On top of that, a smart expat registers in a state like Texas, so if you’re middle class you end up paying little-to-no taxes.
Tax flight does occur, but the billionaires usually move to European tax havens like Switzerland or Monaco rather than the US. >

That’s where rich Americans keep their money too >

Correct me if I am wrong but the United States is one of the very few countries in the world to impose income taxes based on citizenship meaning even US citizens who live in foreign countries are still taxed with the same tax rates as resident citizens. Other countries seem to have no problem with the U.S. using this very different taxation tactic. So, even if the income tax rate was to be raised on the wealthy Americans, I highly doubt they could avoid it by moving out without renouncing their US citizenship entirely.
Also, as seen here, plenty of Europeans have become tax exiles. >

The US taxes expats, but you do get credit for whatever local taxes you pay.  If your American tax rate is 20%, and your French tax rate is 19%, you only pay 1% American income tax.