We just back to FL after a late May to last Friday camping loop all the way out to Idaho and back. When we stay at a private cg we do, make a reservation a few hours out from a cg. Just to keep us from showing up at a full cg. And for that 7000 mile cg to cg trip, stopping at about 37 places, we were turned down once and that was at a cg 30 miles from West Yellowstone. And in that case our second choice was open. We had no problems at any other places. We do make advanced, meaning several day, reservations at COE cg or SP. And the other exception is when we plan a mail stop, staying at some cg to get mail and packages. That we reserve a week or so ahead and check to see if packages are OK.
We also saw no sign of the supposedly over filled cg that many people are claiming.
We did not try to stay at any NP this time. RVTW was very useful this trip in finding CG and other places.