Well, the problem as I see is that there are tons of 'small costs'.
You have to be in melee range. Your source of damage can break. An enemy can cast 'weakness' on you, and suddenly you cannot do anything because your equipment fell off. You have to be constantly upgrading your weapon (or hoping you get a newer better one). You can miss. You can be blocked. You only have access to physical damage. You have almost no AOE damage.
And then there's all the utility you miss by not learning mage skills. Healing, shields, elemental effects, hard cc, etc.