A return to Fallout 3's lockpicking basically. For example - If it's an Adept lock, you need to have at least 50 in lockpicking and the "Unlock Adept locks" perk. If you try to unlock a door without having the appropriate perk, you get the message "you lack the skill to pick this lock" - just like in Fallout 3.
You don't need two requirements for lockpicking ... just make it so that you need a certain 'level' of lockpicking- e.g. 50- to open a certain lock.
Heavy and/if requirements go against the spirit of what TES is about. If we decided to go this path with every perk, for example, smithing would require that you understand how to fight with a weapon (that is, a certain level in one of the weapon perks) and that you are good enough at smithing (that is, a certain level in smithing) before you can improve it. While it would add to the realism of the game, I'm not sure it would add any fun to the game.
What I would like to see: a mod that allows fighter-types to break open chests (whether they are successful or not would rely on their weapon's level- e.g. daedric can open up to 'master' difficulty chests, while iron opens just 'adept' difficulty chests), and a mod that brings back the Unlock spell (which would require that you've reached a specific level in alteration for each difficulty level of the chest e.g. 20 in Alteration for 'adept' difficulty chests).