When I'm camping with the wife, she likes campgrounds.
State campgrounds, County campgrounds, National Forest campgrounds, BLM campgrounds, ocassionally a City campground, even some privately operated campgrounds (usually operated by native americans, we NEVER stay at a KOA or the like).
Allmost all of the public campgrounds that we frequent have the small dirt or paved pull-in or back-in parking spot plus one or more nice tent spot(s) for those that use tents.
We've never had any issues, and we've never been asked to leave because we didn't have a tent.
There are some campgrounds that have "walk-in" camp sites that are designated for tent campers only by a sign and the actual tent location(s) is usually a bit of a walk from where the vehicle is parked. Those are usually a big "no-no" for truck camping in the truck, or any type of "in-vehicle" camping.
My experiences are mostly in the Western 11 States. I've heard it could be different east of the Rockies.