At the beginning when you first get to practice with Miller, dont even bother or worry if you cant do it and break all the lock picks.
You still get the XP (same for any other lock you try and pick) for trying and which goes towards levelling up.
Remember, when you select a " Will you teach me XYZ" option, youre simply unlocking the ability itself. You then need to “practice” (eg, gain XP) to get both yourself and henry better at it.
This is no different to any skill and the learning process involved in real life. 9/10 youre not going to be good at somethinh you just found out about.
This is an extremly logical game in terms of its systems, learning them and the many ways they can be used.
Lock picking nor any other skill is broken, theyre hard because you really are doing them for the first time.
Sensitivity isnt OP on pc or consoles, its that you and henry are both learning to do something new.