I agree with your methods, but not all of your assumptions.
Versatile is free: Yes, very.
Thrown 20/60 is free: Okay, I can get behind this, especially in 5E where "Weapon Focus" isn't quite a thing, but I'd rather have thrown be -1 step. But I also like magic thrown weapons to return, so the property might be worth a little more at my table.
Light reduces damage by one die: Definitely.
Finesse reduces damage by one die: I understand your thinking, but I want to disagree. I can almost get behind the desire to have rapiers deal less damage than longswords; they are lighter weapons after all.
Reach 10ft reduces damage by one die: I agree.
Heavy increases die by one step: I agree.
Twohanded adds two damage dice: I agree.
Simple melee weapons, base damage is 1d8, and Martial melee weapons, base damage 1d10: I'm on board with these.
I think the worst thing is going away from tradition. People like their tradition. D&D players like their tradition. There is something loved about 1d4 dagger, 1d6 shortsword, 1d8 longsword, 2d6 greatsword. A strong part of me wants to resist this. 1d8 damage is fine for one-handed martial weapons, but that makes it harder to balance the dagger as a simple weapon. In my own 3E weapon table rebalance, I priced throwing as a feature and simply took it away from the simple dagger. Darts were "throwing knives", standard knives weren't weighted for throwing. Martial weapon proficiency let you throw daggers, as they do take practice to learn the amount of turns and flick required.
I don't agree that 1d12 > 2d6 is a step, though. I'd rather balance "Great Weapon Fighter" another way.