So far as I know these are the best damage options for each job, counting only self damage, not extra damage from pets and only melee.

WAR - Emp/Mythic(MS Only)
MNK - Relic
WHM - Relic
BLM - Prov Staff
RDM - Relic
THF - Relic
PLD - Relic GS
DRK - Relic GS
BST - Mythic
BRD - Relic
RNG - Relic Gun
SAM - Mythic
NIN - Relic
DRG - Mythic
SMN - Prov Staff
BLU - Emp
COR - Emp
PUP - Mythic
DNC - Emp
SCH - Prov Staff

If you get a bit more specific to the job and its uses, I think it looks more like...

WAR - Emp/Mythic(MS Only)
MNK - Relic
WHM - Cure Pot Staff
BLM - Trial Staves
RDM - Relic
THF - Relic
PLD - Relic/Emp Shield
DRK - Relic GS
BST - Mythic
BRD - Mythic
RNG - Relic Gun
SAM - Mythic
NIN - Relic
DRG - Mythic
SMN - Mythic
BLU - Emp
COR - Emp
PUP - Mythic
DNC - Emp
SCH - Trial Staves

The second list totals at 7 Relics, 4 Emps, 7 Mythics, and 3 Trial weapons. If my numbers are a bit off please forgive me but my point is, Mythics do not deserve the difficulty they have by compare to the others. Even if you are correct and prices on Alex are half of what they used to be (which they are not on Phoenix) then it would still be double the price of a Relic, while Relics have very simple requirements outside of Ancient Currency, Mythics have much more than simply Alexandrites. So explain to me, what exact reason besides having them as a trophy item, should Mythics be so difficult by compare to their fellow high tier 'super' weapons?