FB is not central at all. You do the park in loops, so any place you stay is just central to that loop. For example it's 31 miles from West Yellowstone to Old Faithful, Old Faithful is 40 miles from Fishing Bridge. From WY to Mammoth 48 miles from FB to Mammoth 48 miles. Really not central at all, they are just as convenient just on different sides of the park. Plus WY has none of the downsides of FB and lots of pluses.
agesllaus we've stayed in many campgrounds, we just got good at picking them. Only in FB did kids bounce footballs off our coach or had a dog try and attack us. Never have we been parked that close to another camper. There are better options, even inside the park.