Here's what I thought and was hoping this was going to be:
1) if you hit by 10 or more, you score a critical hit.
aaaaaaand... done.
This way, there's some reward for people who bump accuracy, but it's not too easy to get that it'll happen all the time. Unfortunately, it means that you can't really have a "Down a dragon with a single desperate crit" situation, because in order to hit a creature you still have to hit it.
I don't know that I necessarily like this better than the typical crit. They're really rewarding different things: in the standard rules, they reward dumb luck;my house rule rewards character specialization; the rule posted by the OP is impossible to fulfill (since there aren't odd-numbered dice except by computer, which I guess is okay), but would more or less do the same thing.
Another alternative is to keep the current crit rules, but instead of or in addition to the normal bonus damage dice, on a natural 20 add the difference between the attack total and the target's AC to the damage dealt. This rewards both dumb luck and character specialization, and would make it (I think) more likely to one-shot a target with a crit.