Lemme give you just one example for what I am getting at. According to you, the gate runs the whole show, I as Captain am just a pawn to be pushed wherever I am needed, until I am unchoked and engines running....

Few weeks ago had a deferred APU AND jetbridge had no ground air. 95 degrees outside, probably 110 or so in the cabin, 120 in the cockpit. I politely told the gate agent when we were going to board, so he didnt have peeps sitting in that oven for the whole 25 minute boarding proccess. We were going to wait for the huffercart to arrive, then start boarding as fast as possible.

Well no sooner I get back down to stow my bags (30 minutes prior to departure) I hear him open the boarding door and make the we are now boarding PA. 5 people come down the jetbridge, I intercept them and escort them back to the gate. Gate argues with me we have to get this plane out on time. (yeah all doors closed with no air for 15-25 minutes? no thanks). He says he doesn't need the CA to be there to board, So I get the FA off the airplane so noone is on it and it it would be an FAA violation for him to board.
Huffer cart arrived, I cranked one up while boarding, out in 10 minutes.

That is Captain's authority, not gate agents authority. Lemme ask you this....had I boarded in that situation when the gate agent wanted me to and 3 old lady's and an infant got heat stroke and needed medical attention because they were in a 115 degree oven for 35-40 minutes, who would have gotten in trouble? (hint, not the gate agent)