I find that having a 28 ft total length TT keeps me out of somewhere between 20 and 30 percent of the campgrounds we would like to visit here in the Rocky Mountain area. Believe it or not, there are campgrounds where my 20 foot long truck is over the limit should we be looking to tent camp. For the most part, we prefer camping in forest service campgrounds. Many of them tend to involve miles of dirt road, often quite narrow and overgrown, with access roads not conductive to navigation by a larger vehicle. Just to qualify what I will and won't attempt, I'll add that I'm in general not to squeamish when it comes to towing and have even towed a pop up trailer up and down the Shaffer trail with an S-10 blazer when we were camping in Canyonlands on the white rim trail.
As for national parks, Bryce doesn't seem to have many large spots so if you hit during busy times you'll probably end up outside the park. Yellowstone other than fishing bridge has started limiting total length to 40 if you call to make reservations. GC South rim tends to only let larger rigs into Trailer Village which is just a parking lot. While you can get larger units into Yosemite, the spots for larger rigs tend to be limited which makes getting a spot even tougher in a park that tends to be crowded and hard to get in much of the year. When we were camped in Humbolt redwood forest last fall, folks actually came out and lined up to watch and see if we would be able to get out when we left. I guess even relatively small trailers are considered large there.
In the end, it seems to depend on where you like to camp. If you're looking for a spot with hookups, it will probably be much like a parking lot, and big rigs will probably fit easily. More primitive and isolated spots might not be an option with a bigger rig. There are even quite a few that still only allow tents. You have to figure out what you mean by camping, and what sort of compromises you're willing to live with.