You said exactly what I was trying to say; thinking about a “control deck” in MtG terms doesn’t really seem helpful to me in a Codex context. Each deck always has multiple things it can do, and it’s much more about making effective trades and gaining advantages while trying to read what your opponent is doing.
"Control"ing your opponent is part of that equation, in so much as you want to lock off your opponent’s best options (be that by means of direct "control"y type things like Reputable Newsman or Injunction or Slow-time Generator, or Hero “control” achieved by killing heroes at opportune moments, or tech “control” by blowing up a building right on cycle).