I hate to travel with a schedule for the same reason you indicated; might miss something along the way.
I have found you can usually get sites on a first come basis if you arrive on Monday through Thursday. If arriving in a popular area on Thursday through the weekend then I would make reservations or know that I may have to travel some distance away to find a spot.
We often will pick an RV Park 50 miles or more away from where we would like to be and then drive to see the sights on day trips from the base camp. I don't mind driving an extra 100 miles. If you can get a way from the popular areas it's a lot easier to get first come site selection.