Here's some off-roading in the Daniel Boone National Forest. There are some designated off-road trails, but destroying streams and mudding are very much illegal.
This is just destruction, nothing else. Would demolishing public buildings like museums and court buildings be considered okay just because some people found it fun? Or would communities and the government step in because the destruction of public property is a crime and goes against the public good?
Smoke and Gears: Seeing Through the Off-Roader's Demographic Mirage
This is a great article refuting the claim that off-roaders are just common folk being trampled by elitist preservationists and the big, bad government. The article points out that "motorized recreationists are wealthier, younger, better educated, (and) more likely to work in the professional sector," and that "surveys of ORVers both nationally and in states such as Wisconsin, Colorado, Utah, and Minnesota show that thrillcraft riders are essentially an upper-middle-class group with mainstream family demographics."
Wildlands CPR is a great resource for learning more about the problems associated with off-road vehicle use on our public lands. You can find them at www.wildlandscpr.org