Removing attributes leads to several problems. For example, on the removal of strength:
I have a level 50 character who's really melee-orientated, maxxed skills in armour, block and weapon skill A. However, he never touched weapon skill B.
I have a level 50 character who's really magic-orientated, all magic skills in the 80s or 90s. He's never touched armour, shields or weapons of any kind.
Are you telling me that if each of these characters picks up a weapon from weapon skill B, they will do the same amount of damage with it?
Yes and no. First of all your example is very hypothetical and we know enugh about the skill system to get a bit more specific. We basically know that there are two skills for melee weapons one hand and two hand, but that perks are grouped in axe/sword/mace. Now back to your example. Lets say we have two people Warrior mic one hand and magey mic magic. The warrior has built himself up to be a one handed combat master well magey is built to be a magic master.
They both pick up a two hand axe. Now you would think they are both just as good, but that's not the case. Both have 0 skill in two hand, but the warrior gets some fringe benefits from his one hand skill. To start with, he has more stamina. That is used to make power attacks with all melee weapons. Next, he has the bleeding axe perk from the one hand skill. That perk counts on all axes not just one hand axes. The mage, has nothing. He can't even use his spells with that weapon.