I do my best not to be a narrow minded, my group is better than your group person and I fight that type of thinking almost every day in a dozen ways, specifically around AF canyon. I Mountain bike, Hike, ride my dirt bike, my street bike and Jeep all in AF canyon. I still do it but only on Sundays (used to be us heathens had that to ourselves, not anymore) or weekday mornings.
SXS's have definitely become a major issue in almost any public land in UT. AF Canyon is just too many people in too small a space. I would totally support several remedies.
First- would be to add trails or just limit the current trails to user groups. Designating specific trails for MTB's and hikers only would help the conflict with MTB and Moto guys. But also knock the MTB guys off their high horse when the hikers lobby to get them removed for destroying the trails, just like they are lobbying to remove the dirt bikes for.
Second- would be limiting the number of vehicles. This shouldn't be that hard but government sucks at most things so I have low expectation. There is already a pay booth at both entrances, a counter should be easy to implement. Even if just at AF, not too many people would make the trip all the way around to the Provo canyon side if turned down at the AF entrance.
Third or maybe first - I would fully support a permit that either offered access or priority to people who held it. The permit would not be purchased but earned with service. Give people a chance to clean or improve their public land and only allow those willing to put in X number of hours per year access to some areas. That would eliminate the riff raff and improve the area. It would not be for the rich but for the invested. I spend hundreds of hours per year pedaling or motoing. I'd be more than happy to spend 25 hours doing trail work or cleaning up the places I love if that offered me access to places the ass hats who litter and tear the place up couldn't or wouldn't get.