I live here and have never camped at a place where there was no space because why?
Some campgrounds are county run, some state run, some federally run, and some town run. I would bet that allowing overflow will be completely based on the individual location.
Somewhere like Saylorville Lake's campgrounds could be a hard NO for overflow.
https://www.recreation.gov/camping/campgrounds/233455
But somewhere like Audubon IA which is a random small town, I could see you being allowed to squeeze into a plot of grass on the outskirts of the campground/park.
https://www.auduboncountyia.gov/tourism/parks.aspx