It is only logical for strength to let you put more force behind a blow. The amount of force behind for example a sword thrust could be the difference between causing a light wound or driving the sword through the monster's body.
You don't need to be a fucking superman to run someone through with a sword.
If you can do this already, what will extra str do? Will you push crossguard through the guy as well? Whole arm? Dive whole into the fucking wound creating massive tear as wide as your manly shoulders?
Once you have enough STR to use weapon with no penalties, that's it.
That's why you shouldn't have STR based damage bonus, but weapon based penalties for not meeting its stat requirements.