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This does eventually overtake GWF, but it's a lot more MAD along the way

I think that calculator hides a lot of the relevant concerns here. I think we'll have an easier time looking at things if we look at a constant hit chance (we'll assume a representative 65%; difference aren't gonna warp things that much, it mostly only matters for GWM anyway) to reduce our data by a dimension, and we look at the average damage per normal attack at the fighter ASI levels.

Using the standard array and a +2, +1 race option it's possible to start with +3 in each of Strength and Dexterity. We'll be using that, maxing Strength first, and taking the relevant feat (Great Weapon Master or Dual Wielder) at ASI 3 (level 8) before maxing Dexterity. I'm ignoring the BA attack from GWM. For the sake of comparison I'm throwing in the normal Two-Weapon fighting with a per attack adjustment on the BA attack.

In general we can get the damage of an attack, DPA, as $$ \text{DPA} = h\times(D+M)+cD $$ where h is the hit chance, D is the die damage, M is the modifier (or static) damage, and c is the crit chance.

This works fine for great weapon fighting. However, since the proposed rule (abbreviating at OHA) is a bit more complicated, I'll be calculating it as $$ \text{DPA}_\text{OHA} = h\times(D+\text{STR}) + \left(h+\frac{DEX-STR}{20}\right)\times\left(D+\left\lfloor\frac{\text{DEX}}{2}\right\rfloor\right) + 2cD $$

Now, there's a couple of things to note here. Firstly, OHA is capable of overtaking GWF, but it's investing a lot more. It forces our second highest ability to be Dex, which limits our Con to +1 (you can get that higher with point buy, by dumping your other stats hard). And until level 12, you're putting all that in for a damage output that's trailing behind GWF. If you don't invest in Dex, the damage output from OHA scales from 6.33 to 8.43 which is worse than TWF across the board. Also it's worth noting that GWM's damage increases very quickly against lower AC enemies or with advantage, so depending on factors in-play, the damage might still be worse.

A number of fighter subclasses (and the entirety of the ranger class) use other abilities (eg. Intelligence for Psi Warrior, and Eldritch Knight, Wisdom for Samurai and Ranger) which becomes very strained with this style, wanting a high Strength, Dexterity, Constitution, and the other ability. Two-Weapon Eldritch Knight becomes even worse under this variant.

It also bears mentioning that the base Two-Weapon fighting (assuming your BA is otherwise free which is fairly typical for fighters) is a fair step better than OHA or GWF during T1, and about par during T2. It doesn't really fall off until Extra Attack (2) kicks in at 11th level.

So to answer the question directly, this does appear to close the damage gap at higher levels, but at the cost of an increased rule complexity, and much higher ability investment. And while perhaps less important, OHA still has worse magic item scaling and free-hand economy. Whether the above is worth it will be up to the individual player.

While individual is of course allowed to differ, my suspicion and expectation is that most players who would be put off two-weapon fighting because of the damage fall off at higher levels, is gonna have similar issues with the ability cost of this option. At pretty much par damage this giving up a fair whack of hit points, and is having a harder time picking up relevant 'power' feats like Heavy Armor Master, Sentinel, Crusher, or Slasher, or taking a more evocative ability or feat (to make their character stats less just person-with-weapon), be that Inspiring Leader, Mounted Combatant, Chef, a racial feat, or something else.

So maybe closing the damage gap, but creating an ASI gap, which may or may not feel worse.