Not ignoring it, I already stated Your STR is being annihilated by the AP scaling formula, it looks like a big number compared to a level 15's 70~, but that 343~ STR really isn't that impressive as you think for a level 80. In the actual attack power formula, you effectively only have 100:
f(ATK), (level 80, tank): f(ATK) = ⌊ 115 × ( AP - 340 ) / 340 ⌋ + 100
I have 343 STR (my xaela) at level 80 with no gear & level 1 sword equipped.
(115 * (343-340) / 340)) + 100 = (115*(3) / 340) + 100 = (345/340) + 100 = 101
Contrast a level 15:
f(ATK) formula (1-50): f(ATK) = ⌊ 75 × ( AP - Level Lv, MAIN ) / Level Lv, MAIN ⌋ + 100
min ilvl synced gear, my PLD has 70 STR. Lv.Main for a 15 is 46.
Plugging in numbers: (75*(70 - 46) / 46) + 100 = 139.
That level 15 is getting more from his 70 STR in the damage equation than a level 80 is from that 343 STR due to scaling values and 'base' values which get subtracted during calculations (This is the same reason why you can have 380 DH, but have 0% chance to DH, because the 'base' is 380 which is then taken away during DH % calculations, or how you have 340 DET with no gear on, but it gives you literally zero bonuses). The only reason a level 80 with a level 1 weapon deals more than a level 15 is due to the fact the level 80's WD is worth more per point due to an increased lvlMain attribute and unfortunately there's no way to equalize that while keeping the 80's 343 STR the same which I'd love to test (which I'll agree with you on as far as a test server.) Theoretically if we could mix and match formulas to use the level 15's WD formula but the 80's AP formula, some quick napkin math would show that 343 STR would be about ~28% weaker than the level 15's 70 STR. (101/139) * 100 = 72%
TL : DR, Bigger number =/= always better. 340 CRT on a level 80 is weaker than 100 CRT on a level 15, as an example. The only thing that matters is the relativity between the numbers and scaling values for functions.
That being said, Mikey pretty much covered what else I wanted to say. potency is static. 400 is x2 stronger than 200, it's simple math, and all the formula show it. You could have 1,000,000,000 weapon damage or 1, that 1000 potency attack is going to do 5x as much as that 200 potency one with the same WD.
And when WAR can fling out 1600 potency attacks (Inner Chaos post CRT-DH), Chad will still be doing 3 rotation's worth of Billy's damage in a single GCD (Main + HS is 500 potency, 1600 potency / 500 = 3). You can even go into Synced content and verify it for yourself. I went into Sastasha and fast Blade & Riot blade were doing right around the damages Mikey listed (shocker!). For any given 45~ damage HS ( I checked with a synced WAR), Inner Chaos will be doing ~370 damage (400~ with SE). Again, with enemies that have around 800-1000 health. And that's just the tank alone. Yeah....you can see why the Devs will never, ever listen to such a request.
And you're the one complaining about Standard step doing so much when it only does about 250 damage to its first target in Sastasha when a single lvl 80 skill already does 1.5x as much damage as it? Mutiple level 80 jobs would be able to crush a lvl 15 DNC's output into the dirt if they were given their 80 toolkits. The fix isn't to slippery slope unleash the floodgates and let every job do OP damage, its to nerf skills like standard step at low levels.
Except now you:
1) inadvertly promote people kicking the one guy that's not synced to fish for a guy that is synced so that way everyone can keep their skills, on top of speeding up the run nearly 2-3x over. *clap*
2) promotes ilvl cheesing roulettes since the likelihood of getting a lower level dungeon increases your odds everyone is synced and thus, super fast runs.
3) Addendum to #2, inadvertly promotes making full parties and ilvl cheesing leveling roulette so that way you can blow through an ARR dungeon that was never designed with such hyper-inflated potency rotations in mind in 5 minutes that they can practically afk through than spend 15-25 on a more relevant one. Which means less randos queueing for leveling roulette on their own when they otherwise might have, which could actually hurt queues, much to your assumption otherwise.
Look no further than CT as a prime example of how people will by far and large choose the most efficient method if it is that much better than the alternative, or even Castrum <-> Praetorium.
Rule 1 of software design: You give people an inch, they'll take a mile, time tested unto eternity. You can continue to list ideas, and I'll take the 10s and use my own experience of software development to easily poke flaws in them that the devs would have thought about in 2011-2012 when they were first designing the sync system.
Unfortunately, this topic will continue to be brought up again and again, the exact same points will be spouted, the math will be put out that utterly curbstomps why they'd never implement such a thing, and it'll be a cyclical process. Which is a shame since there's far more important topics to discuss that actually have a chance at being changed/fixed.