I just had one of those moments when you realize that not everyone has noticed the same thing you have.
Tip for speeding up combat resolution in 3rd Edition: Once you’ve identified the AC you’re trying to hit, figure out what number you need to roll on the d20 in order to hit it. Now you don’t need to do math every time you roll: You just look at the die and instantly know whether you hit or not.
The more casual version of that is “lowest threshold”: Did you hit last time? Did you roll equal to or higher than that roll? Then you hit again. Did you roll lower? Then do the math (and, if you hit after doing the math, you’ve set a new lowest threshold).
This obviously doesn’t work if your attack bonuses or the target’s AC are shifting a lot. But 9 times out of 10, those numbers are consistent and the method works just fine.
Also: Roll your damage dice at the same time. If you hit, the damage is right there. If you didn’t, then you just ignore them.