It's actually very simple to stop the court rushing before time expires and the throwing things, spitting, etc.
What did they do to the fan that threw the placard or whatever it was that hit one of the Wildcats? They threw him out. He can't come back. Of course he wouldn't or couldn't wear a disguise---have a friend buy his tickets---or just sneak in. Nope he wouldn't do that 'cause he follows the rules.
What they should do, in my opinion is call a technical on the team. If they make their own team suffer for their bad behavior, then maybe they'd think more about behaving and following the rules. If not, then the universities would make sure that these "FANS" can't get in there.
Sports fans should support their teams and do everything they can to help their teams. That is, everything that is acceptable in society. Throwing stuff, spitting, and other things are not acceptable and not only shouldn't be allowed, but measures should be adopted to prevent them from happening. If these fans are so "in" to their team that they feel they can and should assault the other team's players and or coaches, then they should be put in jail. After all, it is an assault.
These sports programs make money for the universities and help the athletes to hone their skills so they can progress to a job that they want and that will pay them very well. So these universities and the sports authorities should make sure they are conducted in a safe and respectable manner.