So a wizard (base d4) with a dagger (low), does d3 damage. A thief with a short sword (medium) does d6 damage. A Warrior (base d8) with a battleaxe (high) does d10 damage. And you can add fun rules like using a 2-handed melee weapon with one hand reduces the damage one die step. So the same warrior can use the battleaxe one handed for d8. Bows can be created that require minimum strength that grant additional damage (Fine Bow +1 damage step Minimum strength 15).
I see where this is coming from but I don't know if I agree 100%. Why can't a Thief do as much damage with a Dagger (1d6) as a Cleric does with a Mace?
Because in my example, the dagger is a "low" weapon that reduces the damage one step.
I don't mind having different weapons increase or decrease the damage die. But I think that should come in response to an advantage or disadvantage the weapon brings.
See you like the idea too. Some weapons just are better than others. Where I would find this system cool would be in having damage differences based on stance. A spear is great if you can keep your opponent away from you (and devastating if you can get someone to run into it) but once they get inside your reach, it's potential for doing damage drops significantly.
If a dagger is lowering a class by one die type, maybe it's because they crit on 19 or 20.
That's too 3e.
If a battleaxe does d10 damage, then it should have an initiative penalty.
What if you are holding a dagger at the start of the battle and then pick up the battleaxe? A disadvantage that isn't a disadvantage should not support an advantage. (I've played HERO/Champions. I know all about adv/disad systems.
Making a minimum strength requirement for melee weapons is double-dipping. But I could see doing it for missile weapons, as you've suggested. Maybe the appeal of the crossbow is that it doesn't require a minimum strength.
I didn't give any ranged weapon a minimum strength. I gave a special ranged weapon additional damage output in the hands of a strong user.
Truly cool would be changing the whole game so that instead of modifiers for ability scores, dice shifts happened for ability scores. But the game is far developed to make such a radical change:
Strength 10 warrior with long sword does d8 damage (no modifiers). Strength 13 warrior with the same long sword does d10 damage (no +1 for strength, the +1 is in the die). Strength 18 warrior with the same long sword does d14 damage. The average damage is still just +1 and +3 different from the strength 10 warrior. But the max damage is much higher. It's a great idea. But it's not the game Joseph is looking for.