Well, if you really wanna get technical he's a Jim Colletto/ Ted Tollner guy from the early 90's, but he got his big break as a respected offensive coach with **** Tomey at AZ when they went 12-1 in 98 then he became OC which lead to him getting the gig with Slocum at TAMU. Slocum wouldn't have hired if he wasn't well respected & recommended from his time at AZ, which is why he's more of a Tomey guy than anything.
He ran Spread Offenses before he got to Baylor, but his time at Baylor was where he adopted the Leach Air-Raid from Briles, but even Briles was running uptempo Spread as a HS coach in the 90's down in Texas once he switched from the Wishbone.
I agree that we should absolutely be running that system because it both maximizes your offensive passing ability, but as both Riley & Heupel have figured out is that you can create a deadly running game as well. It also alleviates the pressure of having your OL be forced to hold blocks for longer than they're capable of, which is why the pro style O only works with high level road grader lineman (which we don't have lol).
I agree that he learned a lot from Briles & brought that system with him, when he was at Eastern Illinois he had Sterlin Gilbert as his OC who he took with him to BG. Gilbert just like Briles came up from HS football in Texas & was a GA at Houston when Briles was there.