This would render lockpicking useless. Therefore, not gonna happen.
There ARE locks not on doors, you know...like...I don't know, on all those treasure chests and whatnot you probably wouldn't want to bash open for fear of destroying what may be inside?
I think that you should be able to break into doors depending on whatever skill determines strength of physical attack or strength of destruction spell, and also depending on the material and make of the door. This would come at the cost of the stamina or magicka it takes to break the door(which might take more than one door depending on your character's abilities). Some doors though, would be impossible to bust down as they are made of pure thick stone, or the door is enchanted...or both. Also, I think having doors be unpickable would be easy if you make locks that are far too intricate for anyone to do...or the locks are enchanted and only the correct key can open them. Perhaps a text saying "Cannot pick this lock, it is enchanted." or "You are too weak to break down this door." I don't know though.
This would also create a mechanic for doors with variable levels of entry, like weak doors with great locks or tough doors with easy locks, etc. I think it would bring a kind of cool aspect to the game, anyone agree?