I like your premise (modifiers should matter less) but I think your hypothesis (an inverse bell curve solves that) to be questionable. I just don't think it would play very well, with extremely low or extremely high values being common, but mid-range results being rare. Such a system could be described as "swingy" and I think would make conflict feel extremely random and arbitrary.
Instead, I propose that your goal might be better met with something approximating a more logarithmic distribution, which can achieved with a very simple "Roll x dice and take the lowest/highest value" system. I think take lowest probably yields the best results. First a few charts of the distribution, then discussion. Here's a chart to demonstrate 1d20 to 5d20, take lowest single die, as accumulated odds of success. In other words "What are the chances I roll an N or higher?"
And this chart shows the same dice, but as "What are my odds of rolling exactly N?"
So as you can see, the more dice you add, the more extreme the curve. I think about 3d20 gives a pretty nice curve without being grossly impractical to wield. 5d20 gives a very smooth and extreme curve, but seems like an awful lot to sort through. (I did calculations for up to 10d20, but cut off at 5 because any more just seems like overkill.)
So how does this address the premise? Well, if you consider the area under the curve of the Exact Odds chart to be a kind of "worth" for how much a +X modifier of that much is, then you can see that as you add further modifiers, there are diminishing returns for each additional +1. The total amount of value remains the same in the system, of course, but that value is front loaded so that the first few bonuses are the most valuable, while the later ones are less so. So if a player had a +20 then that shifts them into a completely different scale from someone with only a +10. This also means that if a person with +2 is fighting a +4, and they both get a +1 additional bonus, the benefit is greater for the +2 owner.
Really, the big issue is that with a limited range, enough modifiers will eventually overwhelm the value of the randomizer (for any die size, even a d% will run out eventually). This is what "Roll and Count" dicepools like in Shadowrun or the Storyteller system attempt to fix. By treating the modifier level as the number of dice rolled, the randomizer grows with the modifiers, becoming ever more random but offering ever loftier possibilities for extreme results.
So a few final thoughts. One thing I like about something like using take low or take high system in place of a flat single die system, aside from the curve, is the possibility to add other kinds of modifiers into the system. Sure, you can standardize on, say, 3d20 Take Lowest Single Die as your system, but there are many tweaks you can make, even based on character stats. Perhaps you vary the number of dice rolled. In a Take Low system, this veers the results downward for the player, but intriguingly increases the value of higher modifiers. One use for that would be to let players take extra risk at the cost of more dice. Power Attack, for example, can be expressed as "Roll an additional d6 of damage for each d20 you add to your roll". No change in the range, so he's still capable of hitting a DC 12 target, but at slightly lower odds.
Another factor you can modify is how many dice to keep. If you let players take the higher of the two lowest dice, that shifts the curve subtly back up. Or you can flip flop under some circumstances, let players keep the highest die they rolled. Lots of interesting little tweaks to play with!
Speaking of, you may not like the general way this system looks, but consider also the reverse: Xd20 Take Highest. Just flip the Exact Odds chart around and you've got it. Now a +1 is comparatively worthless against the extreme modifier the dice adds. But because the dice cap out at 20, each bonus is pushing that character out of the reach of the other characters. In effect, the modifiers become almost all that matters and the dice can only serve to let you down by not rolling extremely high. This is also a good system for imparting a heroic, high action feel to the game. Natural 20s are the most likely single result! But while heroes roll very high most of the time, when they fall short it is going to hurt!
So I don't know if I swayed you towards a Take High/Low system over some kind of inverse bell curve system, but I hope I've given you some things to consider. I think, outside of what I hope the math demonstrates about probabilities and modifier values, you also see the value in a simple mechanic over a complex one. Ultimately roleplaying is about the people, not the dice, and experience has taught me that a simple mechanic with lower handling time tends to be favorable to a clever mechanic that requires many steps to evaluate.
Note: I made a severe error in my math, which I hope I've now corrected. Let me know if anything looks wrong and I'll check it again.
Addition from 2012-08-09:
An additional variant mechanic: Roll 3d20 but with 1 of them being distinct. This roll actually gives you 4 different distributions at once, which you can use for different purposes! You can do: take low die (low log curve), take mid die (bell curve), take high die (high log curve), or take distinct die (linear). I've experimented with this for 3d10 and it yields nifty results. One example tweak you could use: the lowest die is your value, but the distinct die is your critical hit check. That gives you the lower curve, but retains the same odds of critical hits as a linear 1d20 roll.
Addition from 2014-10-21:
Looking back at this answer, I just thought it interesting to note that D&D 5, currently being released, uses something like the system I describe. D&D has "Advantage" and "Disadvantage," which means to roll 2d20 and take the higher or lower (respectively) die.
