Once that happens, CBP can initiate expedited removal proceedings: you are forced into some cell in the airport, without access to legal counsel or any possibility of communicating with the outside world, in some cases without access to the medications you need to take... until it's time for the next flight to the country that issued your passport. Since you've effectively been deported, you can get hit with a 5-yr ban on reentering the US. And you'll have a lot of explaining to do every time you apply for a visa for any country for the rest of your life, because the "Have you ever been deported?" little question is everywhere.
All this could happen, and has happened. (Not going into the side issues of what it takes for visas in various categories to be revoked, or why Trump's travel ban got watered down: which actually happened for a different reason)
[0] https://www.aclunc.org/our-work/know-your-rights/know-your-r...
But yes, the majority of recipients get them because they're managers at big companies.
Only U.S. citizenship implies a right to enter the country.
EDIT fix typo