Honestly, I think it's this way...
Voters genuinely believe they are picking the best show (or person, whatever...) in the category. But their decisions are swayed by so many other factors.
The Broadway community is ALWAYS convinced, deep down inside, that it's dying. You see theatre folk bragging and celebrating gleefully about how good the hit show profits are, and at the same time there is a little hint of desperation in their eyes and voices.
So, when they vote... there is a gnawing voice in their heads saying... "pick what the PEOPLE want. We have to keep Broadway alive!" Especially when it comes to musicals. With plays, it's not as obviously desperate... because plays NEVER yield the profits that musicals do. There is far less money at stake with their voting decisions, so they are likely to vote with clearer heads (not that they always make good choices though, but at least they're closer to the mark).
Once in a while an "artistic" musical choice slips in with a win (NEVER a sweep), and it scares the Tony voters. They always manage to CORRECT their artsy selves the following season and return to a sane world of voting from the wallet (and the noble cause of keeping Broadway alive) once again.
As far as the "smaller" awards, most of them can't tell a backdrop from a tap shoe, so they tend to vote with the big, popular shows again. They've gotten a little more savvy and educated over the years, but many times they just lump all those "little awards" into one big basket of "we think you'll like this show the best."
"Jaws is the Citizen Kane of movies."
blocked: logan2, Diamonds3, Hamilton22