Not insane, and it used to be commonplace. Departments would compete against each other all the time.
There was even an entire competition organization just for it, that IDPA, USPSA et al pretty much trace their roots to (as I understand it....I'm sure some diehard is going to blow their fucking lid at that statement).
It died out with a refocus of police hiring and culture, as well as austerity measures. That shit costs money, which most PDs don't have any of because nobody wants to spend taxes on essential government functions, but rather social programs. Now, the only widespread shooting competition between police is usually done as part of regional SWAT competitions.