The trick with the d20 is that its binary (at least for an attack roll). I hit or I don't.There's a whole 20 sided dice involved in every action.
Now assuming the damage roll has a reasonable range, there isn't much variability in there. Either I get hit and take some damage, or I don't, but as long as I have a good amount of hitpoints the result doesn't matter all that much in the moment. It certainly might matter for the encounter, but its not going to "shake things up".
Now where things get a little more spicy is with creatures with several attacks (as now we have the chance for 0-4 lets say attacks hitting, that's a big swing in damage), or attacks with a very high damage variance (ie a sneak attacking rogue or a spell with lots of d6s rolled).
However, the real key to why crits work....its the marketing. When a DM says, "I just critted you".....BOOM, instant fear. Everyone stops, conversations end, everyone waits for the damage total. While mechanically crits aren't often that bad, they FEEL really powerful. Their rarity is their strength, and man if you get critted twice in the same round....even if the damage isn't so bad your heart skips a beat.
A d20 roll can't elicit that same response because the results are expected. A hit or a miss....both happen all the time, ho hum, moving on. Crits are special by design, and so they are treated by players and DMs alike as special. There are mechanically other ways to do that, but you aren't going to get the same response by just Widing the range of damage, it simply won't feel the same.
To really provide the marketing of a crit, any new mechanic really needs two things:
1) Rarity: Whatever X is, it can't be too frequent. Scary things happening all the time stop being scary.
2) Build up: One of the reason the crit works is the separation of attack and damage roll. I roll the 20, a crit! Now we wait, the DM rolls the damage, the player waits with anticipation. That build up is a key aspect of the moment. You can't do that with just a damage roll, even if the roll is high, as there is no build up. Sure its surprising when that weapon did monstrous damage, but if there is no "warning" you are about to get wrecked, there's no time to let the fear build up.
Now in theory recharge powers can do this. They can be rare enough (especially if a creature doesn't start with the power recharged). and the recharge roll becomes that moment, the DM announces (Oh, I got my recharge roll!), and now the players have to sit and wait to see how the monster will use it, building that tension.