What I find funny, is that there are only 30 coaches in the league, and 14 of them got votes (and it looks like they all got more than 1 vote too).
That would be like over 200 players getting votes for MVP.
No, not really. You only have one coach per team, but all of them are coaching full time. Of the ~450 players in the league, perhaps 100 carry a workload that will make them a reasonable MVP candidates (30+ MPG). So this is similar to ~45 getting MVP votes -- ultimately, 16 did. The discrepancy is not quite as large.
I don't know man, you decided to filter one pool, but not the other? Really you can filter numbers anyway you want. Why only filter players? I think 4 teams had mid-season coaching changes, only 17 teams finished at or above .500, let's filter those out from the coaches too. So out of those 100 players (30mpg, can I assume 70+ games?), 80 are getting MVP votes?
Even if we use your numbers, only 10-15 players usually get votes for MVP, and I'd say usually about 10 get multiple votes, and usually 5 or fewer got first place votes. If 45 players started getting multiple votes with 40 getting first place votes, I'd find that very odd too.
But let's not argue about numbers (you didn't agree with my comparison, eh not the first faulty one I'll make

). Basically to me it comes down way more coaches got votes then I thought should. 14 coaches got multiple votes, 12 coaches got first place votes. Practically every coach with a record over .500 got a vote. I find that weird, as I would think there would be a clearer consensus about who the top 3 coaches were. Maybe it's a problem with the voting process, the voters, the criteria for the award? I don't know, but I just find the results weird.