A true RPG clearly divides what your character can do from what you can do. Thus, even though you may have cat reflexes, if your character's Dexterity stat is low, he/she should miss most of the time. That is crucial in determining if a game is an RPG or not. Many FPS gamers complained about how you could miss in Alpha Protocol even though the target was right in the middle of the cross-hair or targeting reticule, the reason is that AP was actually an RPG, and your character could miss where you wouldn't. Some people don't like losing this control over the game, and that's fine, RPGs are not for everybody, just like FPS are not for everybody
I would like to argue that objectively, statistical rolls are a horrible game mechanic.
Because they take control, and thus immersion, away from the player, and oftentimes results in games that play themselves.
They basically are a relic from an era when "combat" had to be done by long-division on pen and paper.
Nowadays, combat is done instantaneously on computers.
Also, I object to the whole "choice" in RPG's. In RPG's, you're still clearing out levels. It's just that you're using an outdated vestigial game mechanic instead of a modern real-time mechanic.