Believing that umpires and the AFL don't deliberately cheat or favour teams is not "mainstream", it's just sensible in the absence of compelling evidence to the contrary.
If you do what I suggested and get someone suitably qualified to take a proper look at the data then I'm sure many people (myself included) would be interested.
Two things: firstly the stats that are needed; numbers of incorrect frees given and number of frees missed by particular umpires in a game are not available in the public sphere. They are available to the Umpiring department. They should have the competence to look into it, but haven't.
Secondly, umpires should be beyond reproach - there should be no suggestion of favouritism or otherwise. Playing an umpire with an axe to grind in a game involving the coach who sacked him is unforgivable. That is the umpires department's fault. Perhaps they are naive, more likely too bone headed to accept that there could be that perception.We know soccer has similar problems in Australia; the referee whose girlfriend worked for Brisbane officiated in their final. It didn't matter how well he officiated, there was a stink, and he shouldn't have been there.
A lot of the fault lies with how the AFL makes appointments. Ex players have agendas, yet they have taken up umpiring, umpiring department positions, the match review panel and the tribunal. If they still have strong affinities with a club, they should not be appointed.