Is it common to remove your truck camper at your camp spot?

Yes you can and yea it’s normal. And most TCs can be used, off the truck.

I don't usually take mine off, but taking it off has more to do with how fast/easy it is for you to take it off. With one exception, there seems to be some private campgrounds that don't allow you to remove the TC.

I used to take the camper off the truck all the time. Liked the convenience of being near the ground. After having to evacuate due to a forest fire nearby, I decided to leave the camper in the bed of the truck.

It is uncommon both when I had a TC and now IMO. The height of a TC limits access to about the same degree as a short TT. If I'm not sure...I scout ahead after dropping the TT. Takes a while to drop a TC and reload.

We take the camper off our truck occasionally when camping. For example, when we were in Glacier last fall we took it off so we could drive the Going to the Sun road. We boondock a lot too, but we usually move on after 1-2 nights so it is usually not worth the time/effort to load and unload the camper. We've used the camper on the ground, off the truck for many nights and never had any difficulties. I believe some of the pop-up truck campers are not recommended to be used off of the truck, but I am not certain about that.

I also agree that you would have access to a lot more dispersed camping areas with a truck camper as compared to a trailer.