Why many American workers feel guilty about taking the vacation they've earned?

I've managed thousands of people. In my experience people didn't feel guilt about taking PTO, they felt FOMO because they didn't feel secure in their position or at the company. They felt something would come up or someone would undermine them while they were away that would affect their employment.

I think there's some "grudging acceptance" from managers. "Oh, you're going on vacation on those days. Um... well, we'll still try to get stuff done without you..." And so you feel guilty for going on vacation.

Whether that is deliberate strategy may vary from manager to manager...