What better way is there to determine success or failure if not with probability?
Sure, but implemented how? A roll of a dice is a really reductive and crude mechanism by itself, and in computer gaming it's use is (or was) about technical limitations as much as anything else. A necessary compromise. Today, though, you can take a much more sophisticated approach, where player skill is directly informed by character skill rather than being replaced by it.
A system governed entirely by player skill = my ability to hit this barn door is entirely dependent on my own dexterity.
A system governed entirely by character skill = my ability to hit this barn door is entirely dependent on the roll of a dice, with odds governed by my character stats.
A system in which player skill is informed by character skill = character stats either augment or penalise my abilty to hit this barn door. The amount of dexterity required is entirely dependent on my character stats.
The transition from Morrowind-style combat to Oblivion-style combat was Progress. With a capital P and everything!
(IMHO)