And on that topic, instead of having to hit a certain skill level to pick locks or hack, you should be able to access any lock or terminal at any level, it will just be considerably harder (if not near impossible) to pick/hack until your skill is higher. At lower levels your bobby pins break easier and you have a harder time finding the sweet spot, or you have more junk words and less chances to guess the right one (like maybe one or two).
I would be fine if the minigames were ditched and hacking and lockingpicking would happen via skillchecks - character skill vs lock level with X amount of tries / Y amount of time (say, a month for example) per lock/terminal.
On the other hand, I think the minigamesystem, as it is an easy method, could be controlled via difficultymenu. At easy difficulty you would have a minigame with every lock (in the system you suggested) and terminal and at hard it would be a skill check; locklevel-skill=% that is taken from the skill at the check unless the skill surpasses the lock level - in which case it is a mere successroll with no drawbacks added.
I would also suggest a 2 part difficultymenu - Gamedifficulty & Combatdifficulty (as it was in the previous games) - and the harder you put the sliders the more skill and stat driven the game would become. It wouldn't of course become fully statdriven at any point, but much more that what it would be at easy (which would be something like what Fallout 3 is now at normal).
Very easy game difficulty - noncombatskills start higher, supplies are more plenty and cheaper, minigames etc.
Very easy combat difficulty - combatskills start higher, less enemies/group, lesser chance of encountering higher level enemies early on in areas that are set to be at generally lower level, weapons are easier to repair etc.
...
Very hard gamediff. - noncombatkills start much lower, supplies are scarce and expensive, no minigames at all (purely skillbased lockpicking and hacking as explained above), etc.
Very hard combatdiff - combatskills start much lower and have a bigger effect on accuracy (both realtime and vats), more enemies/group and higher possibility to encountering higher level enemies, guns would be more difficult to repair, guns'n ammo would be more scarce and costly etc.
For a crude example.