In free agency or post-trade, you gotta perform on the field if you're gonna stick.
Do drafting and coaching (don't ignore position coaches) have something to do with it? Yes. Obviously, yes. But if you don't bring the coachable talent with you into the draft, you don't stick - regardless the coaching afterward.
Drafting matters. Given differing decision-making draft input (interference, maybe, where he'd do better if freed up to do his job,) from two disparitively different head coaches, I'll come down on the side of Snead. Trading, same thing. He ain't done all that bad.