I think all this boils down to a misunderstanding of what a roll means in a roleplaying game.
Roll is strictly about whether you succeed in something or not.
So, as a DM, when I set a DC for anything, I first ask myself, "Is there a possibility that this person may not succeed in this activity?" If they will succeed no matter what, no roll is required.
So, in some situations, no roll is required. You either have the strength to lift a rock or not.
However, if I ram myself into a door, will it bust open every time? Is there a chance it WON'T bust open?
It doesn't matter how strong you are, if there's a chance it won't bust open, you need to roll. If there is no chance, and it will bust open no matter what, no roll is required.
Here's the scenario. Door is jammed tight. Dorn the barbarian dwarf slams into it, but he doesn't get a good head start. He even stumbles a bit before slamming into the door. Dang! It doesn't budge. Doesn't matter that he's super strong. He stumbled a bit and didn't get a good crack at it.
Gale comes up and solidly kicks the door at just the right spot where there's some rotting wood on the door frame. Slam! The door flies open. He didn't have a good chance to kick it open, but he got lucky and kicked it at just the right spot so that the rotten wood gave way.
THAT is why dice rolls are so important. They are the unknown factors that you can't see or don't know about. You might be super strong, but maybe there's part of the door that's super strong, and it just so happens that's the part you're throwing yourself into. Maybe the floor's a bit slippery from soot or someone spilled something or waxed that spot too much. There can be any number of unknown factors that are why your super strong giant of a half orc might not succeed in smashing through a flimsy door but the pasty wizard did.
