Or believable
For me, the wizard didn't do anything to earn being better at bashing doors at demigod level. Unless he boosted his Str, he didn't get physically stronger (think Epic Raistlin) and so the door doesn't get any easier to open physically. He DID get better at magic, and he DID get more experienced and better at combat because of all the fighting and combat magic, but he didn't get any practice (in the foreground story or behind the scenes) at building his strength, or least not significant enough to get a +14 to mundanely bash open doors.
In that simulationist sense, the rule as an abstraction is not more real to the player than the fiction it was originally abstracted to model. Anyway, I know you're talking about your 4E DMing experience, but in this 5E thread about Monte's temperature of the rules, I feel so inclined to tie it back to possible implementations of 5E Core or 5E Simulationist edition, but please feel free to ignore me rambling from my ivory tower