Random for monsters is pure fun though. They don't last more than one encounter to begin with, and it makes strategy a lot more flexible. Plus you can catch that guy checking the standard monster manual hp
Until the guy would do enough damage to kill the average, but not enough to kill the random number you generated dies because he couldn't kill the enemy fast enough. Same problem as PC HP being random, just manifesting in a different form.
So? Being able to kill the average HP value should be no guarantee you'll kill the individual monster in question. Variance happens, as does spells, feats or items that boost the monster's hit points anyway.
So... now you have to jack your damage up even more just to not randomly die all the time. Want to have to do triple digits at level 6 just to not die all the time? Probably not. It can be done, but you probably wouldn't want to.
I like how you take something and use it to go off on some self-assured conclusion of your own. Nevermind, I'm not going to argue with someone like that. It's never worth it and they never listen.
I like how you deny facts to talk about "fun" when it isn't especially enjoyable to have the enemy survive at single digits or some other low but > 0 number and then kill you, especially if they'd normally be dead by now.
I'm going to select a level 5 creature at random.
Average: 63 HP.
Range: 42-84 HP.
If you get a weak one, it dies a bit easier but what about the second one, and the third?
If you get a high one, you now need up to a third more damage to kill it before it kills you, because every round you don't kill it is another round for it to do whatever it wants to you. So even though you didn't directly improve its offense, you still did increase the amount of damage it will do, thereby drastically increasing the chance someone dies.
Weapon damage mostly comes from static modifiers. A character at this same level would be swinging for 2d4+13 before accounting for Power Attack and such which will increase the static modifier.