Weapons dealing 1d6 damage

I ran across this argument in favor of 1d6 damage for all weapons (thanks to a backwards link inside a newer post on B/X Blackrazor) and I am very intrigued. Perhaps not enough to totally drink the kool-aid, but instead to have a few categories. Maybe small, medium, and large weapons dealing 1d4, 1d6, and 1d8 respectively? With a few class/race caveats in there?

This particular paragraph really resonates with my philosophy in designing Errant:
Players ask “what’s the difference between weapons?” And I say, “Not much.” They ask what they should use. I ask them what they want their character to wield. I tend to get a lot of daggers and war hammers, strangely enough…as opposed to EVERYONE wielding a damn long sword. It helps players personalize their character without worrying about mechanical advantages of weapon choice.

Arguments against?