If you need archery ( and lockpicking and whether your fireball hits ) to be based on character and not player skill alone, then may I respectfully suggest TES, which has evolved not to be a pure rpg, but a crossover with the action/adventure genre, is not for you and maybe turn-based games would be more up your street. Please, this is not aimed at OP, more at the character skill is all camp.
If you've never played Mount and Blade I suggest trying it now. I'm not sure the policy on linking to websites that could be seen as some as competitors so I won't post a link but you can find it easily enough with google. You can download the full game for free, and play to level 6 as a demo. You might be happy you did, it's a deeply flawed and incomplete game but still a wonderful experience.
Player skill absolutely matters in that game, you won't get anywhere in the harder difficulties if you don't have skill (especially since going up in levels doesn't give you extra hit points), but your character skill is also extremely important especially with archer (and horse archery in particular).
The game also rewarded you with more experience in that weapon. It might take a dozen close range shots to some infantrymen's torso to get a point in archery, but if you get a headshot on an enemy cavalryman from 150 yards away while you're at full gallup on your horse you might get 4-5 weapon points for that one shot.