Why not an extra damage die per level over 1?"
He don't know me very well, do he?
I'm pretty adamant about keeping damage dice under control. That's why I use the "all weapons do 1d6 damage" approach. Sure, I do allow 2d6 or 3d6 for spears and pole arms receiving a charge, and two or more dice for stuff like siege weapons or cannon. But the martial arts monk got only half a point of damage per level... for one weapon! Why on Earth would I give a full die of damage per level to anyone?
Now, I might not be too averse to one change in the combat rules for fighters. You may remember that I regularized the way I handle monster damage: creatures of more than 4 dice do the same damage as an ogre (1+2) and larger creatures do 1 die of damage per 4 hit dice. That's another reason not to let Heroes do the same amount of damage as a Purple Worm... but, conversely, it might not be too bad to make the benefit go both ways: Heroes would do the same damage as ogres, and Superheroes would do the same damage as giants.