Many places do have a per-person surcharge, often up to a higher maximum. Vermont works this way: the listed fees are for four people, as I recall, and then it's a few dollars more per person over that to a maximum of six or eight, depending on the site size. Some also (or instead) permit more than the listed maximum if part of the same immediate family.
Other times, it's necessary to "occupy" two camp sites, even if you all stay on one most of the time. That's actually not entirely unreasonable in my opinion, as the site limits are often at least partly based on things like building codes or overall occupancy limits--the campground can't have more than x people staying there altogether due to the size of their septic system or whatever, and that gets divided down by the number of sites they have.
I'm sure there might be one or two campers who lie about the size of their party, as well.