I'm in the U.S. and I still have to click all those super annoying "Accept using a cookie" popups everywhere. So that EU law certainly does affect me a U.S. citizen interacting with U.S. companies.

The only ones you have to blame for that, are the companies to show you those annoying popups. They have no obligation whatsoever to show that to anyone outside the EU.

Start complaining to those companies and stop pointing your finger in the wrong direction.

That is because it is cheaper to show it to everybody. Not because EU would demand it to be shown for Americans.

Also, law do not require it to be shown for all cookies. Only for tracking ones.

To nitpick, while for non-EU companies GDPR applies to individuals in EU (and their data) as per GDPR article 3.2, any EU companies have to apply this for all personal data as per GDPR article 3.1.

So while foreign companies can decide whether they want to apply their GDPR policies (which generally should not require "cookie banners", though it is a popular choice) only to people in EU or all their users, an EU company does not have a choice, they have the obligation to treat personal data of Americans and Iranians and everyone else in a GDPR-appropriate manner.

Keep that in mind the next time you encounter a US based newspaper that puts up a GDPR error page instead of serving the news article you requested. The EU asserts it can penalize a US based company a percentage of its worldwide revenue (not EU derived revenue) for GDPR violations.

I'm not saying it's right, I am saying that these are the logical, practical responses to the way different jurisdictions expect their laws and regulations to be honored, respected, and applied.

"The EU asserts it can penalize a US based company" ...

Well, of course it can, if the company violates EU law inside the EU. Do you think US law trumps [sic] national law globally? If a US company doesn't want to comply with GDPR, it is free to cease trading in the EU, or cough-up the fines.

Extraterritoriality is an old US habit.