I think it's okay, but I don't think I'll actually implement this into my games. At a first glance it buffs some classes while nerfing others.
Classes that focus on light armor & dexterity might have a higher percentage of characters that dumped strength, meaning that they will never be able to achieve a +3 light armor in game, because they would have to bump their strength to 12 in order to upgrade to medium armor. That late in the game, an additional +1 to AC might not be completely noticeable, but it could mean for a rogue or a ranger that is a bit more slippery than they could have been. I've focused more on light armor here, because medium and heavy armor seems to be rather easy to come by for any character that would have higher than a 12 in their strength (typical barbarian, paladin, fighter, etc.)
When it comes to the weapons aspect, they seem, for the most part, fine, but similar problems pop up. A dual wielding character who wanted to choose double handaxes is now seeing 1d4 dmg instead of 1d6's as you can only dual wield light weapons unless you have picked up a feat that says otherwise. For Ranged, a longbow now requires 13 strength which a dex-based Rogue/Fighter/Ranger might not have. While it's more realistic in the sense that bows require a /ton/ of strength, it nerfs the character who either has to go MAD at character creation, or spend ASI's on strength in order to get that longbow while STR-based characters or spellcasters aren't having the same issues.
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