What would banning people from these areas achieve? Sure, you'd have an unspoilt wilderness, but...for whom?
The easily accessible areas are a tiny part of America's public land. Litter and vandalism don't significantly damage the local ecology in somewhere you already have hundreds or thousands of people passing through even with a leave-no-trace policy: they mostly make it less attractive for other visitors.
I'm not arguing that people should vandalise or litter public areas, or that the likely practical response wouldn't be to close affected areas. Just challenging the assertion that this would be a useful thing for the likes of the BLM to do. One possibility is that by closing them to RVs you keep them available to walkers on day trips or camping in tents, who may cause less damage if only because they can carry less stuff.