The fact that there is no correlation between skill/attack rolls and damage output has always bugged me.
You roll a 19 to hit? Awesome! Too bad you rolled a 1 on your damage. Better luck next round.
There is a direct correlation:
Increased skill/attack rolls leads to increased chances of hitting leads to dealing damage.
Example:
PC A has +5 attack, B has +10 attack, both deal 1d8+4 damage and are attacking AC 16.
Ignoring crits, the expected damage of A is 4.25 per attack, but B is 6.375, over 2 points better per attack.
So, the additional +5 on the attack roll of B over A directly impacts damage by increasing it by more than 2 points per attack.
That is the direct correlation.
Will both hit on the same roll of 19, sure, but one misses on a 9, and the other hits. As I said upthread, the attack roll is (and was meant to be) binary: hit or miss. Adding the crit on 20 messed it up and got people thinking that "the higher the roll the better" which really isn't the case.
You could
make it the case, but then you are "double-awarding" higher attack bonuses both because you are more likely to hit
AND adding even more damage on a lucky higher roll. Not something I think is necessary, but if you want that, as others have posted there are plenty of ways to implement it.
Personally, I would rather see crits based on hitting by a certain amount instead of natural 20.