The only issue I have with the OP is that strength also determines what armor you can wear. Beyond that melee is broken. It's an AP thing. The amount of AP it costs to move close enough to hit and then swing is crazy. The Only way to remain useful is to pump up Speed which of course makes you Very Very weak as you will of course have much less HP and will do less damage.
I can think of many solutions however I am not the Dev so what's the point.