Noted. We've had this conversation before
I think I wasn't clear enough. I basically agree here--having one mechanism (d20 + modifiers) over many is a great improvement. I don't want a bifurcated system, but if there is I'd rather put that elsewhere (among the different mechanical elements) instead of using different dice. I don't think that using different dice really adds anything.
I find that an obsession with statistics and theoretical probabilities is a detriment to a game system. The difference between a flat roll and the bell curve of 3d6 is small over the expected number of comparable rolls during a session. How many skill checks do you make that have the same modifiers (including circumstantial ones) and the same DC? Certainly not enough to invoke the law of large numbers. The ballpark number for that (where you can reliably tell a bell curve) is somewhere around 30--that's 30 observations drawn from the same distribution including modifiers. That means that, for me, the type of dice you roll all comes down to simplicity. If you're going to roll a bunch of them, do something simple (2dX at most). Shadowrun-style massive dice pools involve either automated dice rollers or lots of time spent counting dice.
I very much believe that trying to be "accurate" by having detailed rules is a trap in game-system design. Tighter rule-sets can't actually portray the underlying fiction that much better, and in exchange you make things complex and make the game about playing the rules, not the fiction. The more I play the more I appreciate lighter, more modular systems with fewer interacting parts. As someone said above, having "just like X, but..." means that you have to know both sets of rules. Flatten that exception hierarchy, please!
Edit: And Quertus, I realize this wasn't intentional, but that opening couple of sentences came across as really condescending and belittling. "I'm sorry your players are morons stupider than 7-year-olds."