The real answer is that it's purely a game construct, to prevent finesse-type fighters from being terrible in melee combat. There was a big problem with finesse-type fighters in 3E, where they could spend a feat in order to make their attacks accurate enough, but there was nothing they could do to increase their damage to a meaningful level.
Remember, 3E started the trend of massive HP inflation, so fighters needed that extra damage in order to keep up. Rolling 1d6+0 for weapon damage was never going to drop a level-appropriate enemy. Sure, you could land a hit, but if that damage is trivial then the whole endeavor is a trap option. With 5E giving Dexterity to damage, at least finesse-weapons are no longer a trap.
It's just that their hand-wavy semi-abstraction raises more questions than it answers. If skill matters, then everyone should also add Proficiency to weapon damage rolls. And it's not like precision renders force irrelevant, so really everyone should be adding Strength and Dexterity and Proficiency to damage rolls... but that gets complicated, and it makes the math harder to balance, so they err on the side of more-balanced gameplay that doesn't make a ton of sense for how the world works.