Unless it's a melee weapon it would make absolutely no sense to do less damage if you're lacking the strength.
Speaking realistically, yes. But in terms of gameplay, from a certain perspective, it does have its logic. Since maybe they figured that just reducing accuracy wasn't a strong enough pentalty. Plus, most likely, your skill in a weapon still increases its damage like in Fallout 3, so it would make sense that not being good enough to use it effectively would reduce it, I guess.
It's a perspective I can't agree with, mind you, since I am generally against the idea of stat requirements for items in games. I shouldn't be magically unable to hold a gun at all just because I'm not skilled enough to use it effectively. Then again, if Obsidian had the sense to not make it a hard requirement, I guess it's not entirely terrible, if I'm not good with a gun, I expect to fight less effectively with it, I just don't like the idea of there being some arbitrary limit on stats which, if not met, causes the weapon's effectiveness to suddenly drop a really large amount. Though considering that weapons that the big guns skill no longer exists and weapons formerly handled by it have now been moved into other catagories, I guess it was a necessary evil to stop a character who has no business using a minigun from being just as good with it as with a 9mm pistol.