I am not a Math Wizard but your Math-fu is broken....
Okay lets be serious.

First you say 20 % dmage increase but you dropp the rest ? You get a crit chance increase of 15 %. Next is you are crit hitting and direct hitting sometimes even without the essence Bonus, then some bosses have a increased damage gain against certain damage types, essence interaction, Rotation, Job, etc.... with all that your Math is just incomplete and more or less a guess and has nothing to do with facts.

So you will say now but you dont have facts either !
Yes but as many people here explained we have a "prima facie evidence". Evidience that results from expierence and repeatet results. To put a simple "Esence use = faster runs".
I did runs with many people not using anything and perform at mechanics very poorly and the runs took 40 to 60 minutes, while on the other hand runs with many people using essences the runs were between 18 and 25 minutes. This leads to a conclusion based on expierence.

I am not sure but "Fact's" are rare and hard to provide because they are absolute cant be denied. So if you have facts then provide ? And dont tell me your "i am right, you are wrong" or "you are ignoring ..." or "12 seconds " because that are not facts.