If I can be honest with some people here, the "I don't pick the locks, my character does so I refuse to do the mini-game" doesn't seem right. It may not be you in Cyrodiil, but you do control him/her.
You still decide where he walks, even in combat when he swings and such. So to decide all that and influence all the battles and then suddenly not doing the minigame seems weird to me. Sure you want him to be able to pick locks because of his skill. But even in combat, you might have a really low blade skill but you can still dodge and block and jump around while trying to get hits in. That's exactly the same thing.
Sorry guys, but that's just my opinion.
And you're welcome to it. It's your game.
My opinion is that the mini-games (persuasion and lockpick) are meta-games. They violate the concept of role-playing. Any player can learn to pick any lock, regardless of the character's skill.
In combat, I may trigger the action, but my character's skill set determines how effective it will be. If my character is a novice with a shield or bow, then fatigue will affect what he can do, and how long he can do it. If he is advanced, he will be able to jump higher, dodge effectively, shield-bash, disarm, etc. He will also hit harder, if he is experienced.
It is not exactly the same thing. It's completely different.
The auto-pick button is actually the lock-picking anolog of clicking the mouse to swing the sword. You're telling the character "do this," and the character does it, within the limits of his skills.
And that's just my opinion.