Thinking About Game Design- Dice Plus Stat VS Dice Pool and Successes- Your Thoughts?

As a fairly experienced gamer in a wide variety of genres, both in RPGs, board games, card, and miniatures, I began to wonder how mechanics are chosen.  For example, why the 2d6 + stat in Warmachine, or the multiple d6s in 40k.

I’m no statistician, but I’m curious for those who are mathematically inclined, why is one mechanic of dice rolling chosen over another?

Are designers trying to get a smoother bell curve for averages by using a dice pool, counting “successes” when a target number is reached versus something like the D20 that’s used in D&D, Dark Age Games’ Dark Ages, or the d10 in Infinity or Reaper’s Warlord?

When a designer decides upon a mechanic, is the mechanic designed to fit the theme or idea behind the game, or is the game designed around the mechanic?  I’m sure it can be done both ways and has been.

Also, to send the feelers out, what seems to be the dominant mechanic out there?  Roll one or more die and add a stat hoping to beat another stat, or is it the dice pool method of rolling several dice trying to reach as many “successes” as you can?

To further the question, what do you prefer?  If you had a chance to work on mechanics for a game, how would you design the mechanics?  Is one way easier than another?

I just wanted to pose those questions to see what everyone thought.