I have a 32' motorhome and have had very very few problems with getting sites in national and state parks. In fact, I often see 40+ feet long rigs parked there. Tip--in Grand Canyon south rim, stay in trailer village inside the park. Near shuttle stops, full hookups, and lots of friendly elk wandering around!!
I have also stayed at Yellowstone, Zion, Yosemite, and a bunch of others with no problems.
As a test, go to recreation.gov and look up each park. Type in test dates and select Filters, and then enter RV motorhome and your length. It should give you a list of sites that your vehicle can fit into.