In defense of "lockpick" minigames!
So, you've got an action that you want to be gated, such that you can't automatically succeed at it, but isn't itself core gameplay. You can:
(1) Unlock it based on character stats
(2) Percentage chance based on character stats
(3) Minigame with difficulty based on character stats
(Also, various combinations thereof, such as minigames that you need a minimum stat to even attempt)
Of these options, I prefer the third.
Option 1 tends to feel arbitrary, as the stat you need generally increases in such a way that it's difficult to know when you need to invest and when such investment would be wasted. Still, this would be my second choice.
Option 2 is incredibly annoying. Nothing makes me decide to save scum like failing a 90% chance to get a significant upgrade.
Option 3 does a bunch of things right: (A) the difficulty you're having with the games is constant feedback towards whether you want to invest in them, (B) with save scumming you still have to complete the challenge you failed, and even (C) it's a nice break from the usual gameplay. The danger, of course, is that fans of the "larger" game may very well not be fans of the minigame. So, you could do something that many examples of the genre do in fact do: make it optional. You can simply spend a quantity of some other resource to successfully skip the minigame.
Admittedly, my opinion is colored by the fact that I mostly enjoy these little games, some of them a great deal. I even liked Bioshock's pipe dream.