On pavement, yes, turning while moving (on pavement) by definition damages a 4WD engaged / locked differential drivetrain and tires, because the system is forced to move all wheels at the same speed, thus either the drivetrain takes the force, or more commonly, the wheels skid (shedding tire material), which leads to unsafe driving conditions on the road (imagine turning the wheel and your whole car starts skidding).
The benefit of 4WD is when there are loose surfaces (like on gravel) and you actually want all wheels engaged like if 2 or even 3 wheels are off the ground.
during 4WD rock crawling the tires do get ripped to shreds very quickly, but you get the advantages of being able to climb almost vertical rockfaces and drive through rough terrain.
Through all this drivetrain talk, I hope you understand why Park Services would want to enforce 4WD - because AWD and 4WD are fundamentally set up to do entirely different things. And it's not right to say "4wd and awd are the same"