I pay extra if that is the fee structure.
Most of the public campgrounds I use, there are different classes: tent camping areas, designated tent sites, designated RV sites. RV sites may be in separate areas from camping sites, and there may be multiple classes of RV sites, whetther primitive, electric, water/electric, full hookup, paved vs unpaved, and pull-through vs back-in. All these classes can have different fees, the principle being the more services you buy, the more space you buy, the more you pay. A 50 amp site might be higher priced than a 30 amp site, even if you ate plugging in only 30.
It is not usually about what you bring, rather what you take. A tent in a full hookup RV site pays for a full hookup RV site. A RV might be parked in the parking area of a designated tent site, no hookups, and pay the tent site fee. I've found it common to have "second unit" fees, e.g. if you put a tent on your RV site with your RV, or two tents in one tent site, there will be an extra fee, but not the full fee for a tent site.
There are also "extra persons" fees and pet fees in many public campgrounds.
I've not yet seen metered utilities in a campground, most do not permit extended stays, a daily charge for the utility seems to fit that need. Public RV parks, however, may differ. I've seen metered electricity in city and county RV parks, for sites occupied long term by seasonal workers (harvest, planting, powerplant maintenance, Christmas rush at Amazon, etc).
If you are seeing only one price, there is likely only one type of camping in that campground, or else you aren't seeing the whole fee structure. I've found that National Parks often have different facilities by campground, rather than by campsite. Many have no utilities (some don't even have water in the campground) and might not even have designated campsites. Been where you just pick a spot in a big open area and pitch the tent or roll out the bedroll.
Tom Test
Itasca Spirit 29B