I am with Guppy on this.
Without having brake temperature gauges fitted to the 737 it is difficult to judge how heavy we are on either foot. I used to be left foot heavy on a jet without autobrake but corrected this because we had temperature indicators.
Autobrake is applied on mainwheel touchdown quicker than my reaction would be to start applying them manually. However, I will usually be manual braking by 90/80kts to modulate enough to find a convenient runway exit.
To apply the brakes early in the landing roll would mean better heat dissipation at speed rather than leaving it late on. I don't understand why you think this would mean excess heat build up?
Beginning braking at the point of touchdown is a method accounted for in the performance calculation. I have yet to see anyone start applying brakes manually at that precise moment. But perhaps that means I am not one of the "good" pilots you refer to. Are you a simulator or line trainer out of interest? What is the opinion of your Head of Training on the subject?