Looking at your numbers it looks like if everything were distributed equally that's about 42% Str, 58% Dex.
You actually have that backwards. If and you assume all Barbarians and Paladins are Strength and all Monks, Rogues and Rangers are Dex the numbers would be:
Strength martial: 21.5% of all characters (Paladins 7%, Barbarians 8%, half of Fighters 6.5%)
Dex martial: 31.5% of all characters (Rogue 11%, Ranger 7%, Monk 7%, half of Fighters 6.5%)
Looking just at martials that would be 59% Dex, 41% Strength.
However, I would guess Monk is probably less popular than most of the others?
Monk is 7% of PCs, which is the same as Paladin and Ranger, slightly less than Barbarian (8%) and substantially less than Fighter (13%) and Rogue (11%).
Here are the most popular classes, top to bottom based on DND Beyond numbers from 2020:
Fighter
Rogue
Warlock
Wizard/Babarian/Cleric
Monk/Sorcerer/Paladin/Ranger/Bard
Druid
Artificer
That tracks fairly well with my experience. I would say Barbarians are less popular in games I played than indicated here and Rangers are probably more popular than indicated, but otherwise this is consistent with my experiences.
And this is ignoring magic weapons, which skew melee.
That does not affect what people play, moreover melee does not mean strength.
It may be true to say magic weapons skew melee, but I do not think it is correct to say magic weapons skew strength, considering daggers and shortswords are among the most common melee magic items and all ranged weapons use dex.
If you break it down into 2 groups:
For strength based weapons you have:
All melee weapons plus Darts
For Dex weapons you have:
All missile weapons plus Daggers, Shortswords, Scimitars, Whips and Rapiers
I don't know that the first list is more common than the second.
It also ignores the feats. Polearm feat is one of the stronger ones and combines with Sentinel and Great Weapon Mastery to make it a very powerful martial option.
Again, I don't think this affects what people play.
Also I have been underwhelmed by this combo in play, especially when magic weapons are considered. While it is probably true that there are more magic melee weapons (to include finesse versions), magic Glaives are Halberds are not common at all and you really need one of these to get the most out of those 3 feats.
Generally considered more powerful than the crossbow expert and Sharpshooter, even with Elven Accuracy.
I would not agree with this, especially since it is 3 feats vs 2 and the +2 attack bonus from Archery has a big effect on how often you land the +10 damage. I think Elven accuracy is generally going to be less effective than a Dex ASI for the 3rd feat.
Looking at a 16 Strength PAM/GWM/SEN or an 18 Dex XBE/SS at level 8 and comparing these two in damage vs 16 AC:
PAM/GWM/Sentinel/GWF with reaction attack: (12+3+6.3+6.3+6.3+40)*0.3+(3+6.3+6.3+6.3)*0.05 = 23 DPR
PAM/GWM/Sentinel/GWF without reaction attack: (9+3+6.3+6.3+30)*0.3 + (3+6.3+6.3)*0.05 = 17 DPR
SS/XBE/ASI/Archery: (12+3.5+3.5+3.5+30)*0.45+(3.5+3.5+3.5)*0.05 = 24 DPR
So XBE/SS is doing more damage vs an average AC at this level even when the Sentinel gets a reaction attack.
If we are really talking about optimizing damage in melee range I think a max charisma, 13 intelligence, 14 Dex V. Human Hexblade X/Bladesinger 6 in medium armor is I believe the highest DPR available using Bladesinger extra attack with Agonizing Blast, XBE and Sharpshooter.
At 8th level that is 2d6+2d10+20+4xCharisma base damage. It is 4d6+2d10+10+3xCharisma when you cast/move hex and 6d6+2d10+20+4xCharisma when the target is already hexed. You also typically will have Armor of Agathys to cast using Wizard slots on this build. Against 16AC with a 16 Charisma this is 20, 21 and 27 DPR respectfully.
At 11th level it is up to 2d6+3d10+20+5xcharisma and 5d6+3d10+10+4xCharisma when you cast/move hex and 7d6+3d10+20+5xCharisma when the target is already hexed. You will also generally get Eldritch Smite at this level.