Sooo, what happens if one takes the route that's not approved?
Nothing, apparently. About one year ago I took the longer ride / shorter hike route - I had no idea that was "not approved" - and I lived to tell the tale. There are closures of Cottonwood Canyon Road from time to time (in fact, they closed it one day after
my non-approved trip last year). Maybe that is what makes it non-approved?
BTW, I did the drive in something in the Ford Escape class of vehicle, and there were some slightly dicey spots, but nothing you couldn't negotiate with a little care.