Things are changing.....the RV industry is booming and people are traveling because of cheap fuel. If you're going on a trip that includes National Parks, that means you'll be camping in or near them. That's going to REQUIRE some planning. We just went to the Grand Canyon last week, school was back in, the weather was cold, yet everything was booked already, months in advance.
No offense, but you really can't take advice from people who are full timing because they camp differently. They have time to decide and book where they will stay or will typically stay quite a distance from things like National Parks.
Anything that's going to be near a park on a weekend, you should probably call and make a reservation. If it's a week day and not a popular area, we like to pick the town where we will be staying and then look it up in RV Park Reviews. We copy down the two best places and then call them the morning that we are heading there to make a reservation.
Keep in mind, many who are telling you that it's no problem, are not doing the type of trip you are....visiting National Parks. You also need to decide if you're willing to take a chance and stay at some meth lab campground, because that's all that will be left if you don't do some planning.