Part of the reason he never punts is the inconsistency of HS punters, so whatever formula he's using factors in the likelihood of not netting a ton of yards on a punt. I bet he'd punt more often with a decent college punter.
I like your idea of the rugby style punts with an option for a fake every time. There's got to be some reasoning why coaches don't do this more often because it makes perfect sense on paper. It's frustrating how often I see punts in college/NFL where the punter could have walked for a 1st down if he had looked up.
As for the BYU play, I admire the call. It was executed atrociously, but I don't mind taking the risk when the defense won't be expecting it if you have a play you're confident can be executed. I've always thought a brilliant fake punt call would be to take the delay of game on a 4th and 4 from the opponents 40 under the guise of getting a few extra yards of room for your punter to pin them deep. Then run the fake on 4th and 9.