I also quite like dice pools, when used reasonably. I like the core d20 mechanic too though. At its heart, it's just a way of resolving a percentage chance of something succeeding, and it's the way that bonuses interact that always cause problems with it.Take the simplest possible check, you flip a coin and want to know if it lands head or tails - roll a d20 and beat DC 11 to land heads. The problem comes when we start to scale things up - if you make a strength check with d20+3, you can't get less than a 4 and you can now reach 21-23, and we give this meaning.
We could consider limiting all DC/AC/etc in the range 1-20 - now there are no special numbers that can't be reached by people with very high skill checks and we can give out all the bonuses and penalties we want, your chance of success remains between 0 and 100% in 5% increments. This is unnatural at the ends of the distribution though, we always want a chance of success and a chance of failure, and you can't do that so well with a single dice plus modifiers. No, a bell curve is more natural to us because most things happen within the range of a single standard deviation. Could we mimic this with a d20? With exploding dice perhaps, since each 1 or 20 takes you further outside the first standard deviation in a strange discretised version of the distribution. We might also want to consider other ways to modify what we actually roll - advantage/disadvantage changes the shape of the distribution but doesn't recentre it, whereas say, halving the modifier you add to the check equally affects two different bonuses in a way that applying a -2 to both doesn't.