And, as other posters have said, Strength is tied to lifting, but other than that it is just melee damage. And, I believe if we wanted to go full simulation then you would need to apply Dexterity and Strength, because you need to be able to aim and to hit, and then you subtract the damage type from the armor type, and we can make this super complicated.
So, maybe the Goliath gets a bonus to lifting things (is stronger) but isn't as accurate in his sword play so he doesn't get to double his melee damage. It isn't "stronger without being stronger" it is stronger, but less able to leverage their strength in combat. This isn't nonsense, it is dealing with an abstracted system. Not everything is 1 to 1. Heck, even a +2 INT doesn't actually make your character smarter. It just makes you better at magic.