The Agile Fighter feat shouldn't be a thing. That's just overpowered. And defeats the purpose as noted above.
I would just remove +DEX to any and all weapon damage, and make STR the ONLY attribute to ever apply a modifier to weapon damage. That means finesse weapons AND ranged weapons, and that includes a negative STR modifier. Kill all 8 STR archers.
Also, crossbows shouldn't add any ability modifier to damage, period. Make a new weapon property called "mechanical" that prevents ability modifier to damage. And as small compensation, increase damage dice for all crossbows by one size.
One handed swords, cutting/slashing weapons should all be finesse. Cutting edge weapons are about control and only a few pounds of pleasure are required to be useful. However, they are virtually useless against strong armor that convers the damage into concussive force. Its not that it shouldn't be a thing, its that it should be more distinct from strength attacks. If slashing was dex -2 damage vs heavy armor, piercing was strength (melee) or dex (ranged) -2 to hit but critical on 19-20, and bludgeoning was strength no adjustment then players would have more interesting decisions.
THE REAL PROBLEM is not dexterity in combat (they are all about the same in combat attack and defense as strength allows plate it also adds to armor), its the out of combat functions that convince players to pick dexterity. A lot of the player at my table want to sneaky (
stealth) as result they want dex, which makes strength being equal wasteful compared to more interesting alternatives like wisdom for better perception which is also important when trying to avoid guards.
Stealth is the #1 reason for dexterity player characters which is a
narrative choice. Their is no amount of nerfing dex that will make players at my table not want to play a medieval batman. They are the darkKnight. Its fun, I get it. Also, the white knight gets shunned because the party is trying to sneak in and you have one guy in with shinny armor "playing the symbols" as the go in ruining every attempt at stealth. So when they make their second character they go stealthy to avoid "bringing the group down" or alt least Barbarian so they have good AC with disadvantage to stealth for armor.
No amount of nerfing dex with change that. Strength will never be the stat for stealth and players are more likely to go with a spellcasters stat and constitution. (Example: Shadow Sorcerer with CHA and CON so they can take subtle spell, greater invisibility, and shadowblade)
If you want to get a player to pick strength and not dex you have to make strength better and sell them on the idea. Watch Conan then offer to help them build a new character. I would not be surprised if the number of barbarians increases.
If you want to
Fix something, give strength more utility.
Encumbrance (carrying heavy weight is a fundamental use of strength many GMs like to hand wave)
Javelin's can use strength for to hit and damage as a range weapon.
Having a 16 or higher strength negates the reload property on Crossbows
Intimidation skill can always use strength as the attribute
Ensure players know the Grapple and shove actions
Ensure their are as many strength tests as dexterity checks in a dungeon. (Climbing, stuck doors, rusty levers, weight bearing traps, push/pull puzzles, and requirements to move heavy object A to room 3)