Why solely on character skill. The OB system had huge flaws, notably very hard being easy, but it was affected by character skill, the tumblers slowing down as skill increased. If the difference between v. easy and v. hard was greatly increased so you had virtually no chance to do the hard ones at lower skill, but might just get lucky now and then, the auto pick disabled ( run out of patience, then you ain't picking no locks ) and it was in real time then we might have a system that works. Personally I loved the FO3 mini game but hated the skill restrictions. Yeah, I know it's a very hard lock and I'm not a master at picking, but I'm an expert, and you're not even gonna let me try?
The lock picking in Oblvion didn't rely on character skill, if it did you would have to have some character skill in lock picking to actually pick a master lock. Slowing the tumblers down didn't affect anything, especially if you have an unbreakable skeleton key.
To answer your question, NO you should not be allowed to pick a lock unless you have the right skill level to do so. Again, what good is having skill levels and increasing them if you can bypass them all together, like the lock picking in Oblivion?