Blue mage shouldnt be "Limited"

[ForteNightshade]

so without basic instinct buff, the parse would be cut in half. it would be 16k burst dps and 7-8k stall dps. comparing it to stormblood, average dps for a caster would be 10-14k. With that said, most casters can also out heal for a fraction of the cost of blue mages white wind. Thay can also out heal single target heals blue mage has.
blues aoe heals also have a shorter radius compared to healers and are ineffective unless in healer role.

blue mage isnt over powered, it parses less than last expansions dps (without the solo play buff) its heals are not as powerful unless you go full healer(then they can heal but not as good as an actual healer) and blue mage tank constantly loses agro (on the fact that they spam diamond back as often as they can before running out of mp and dying.)

if you have doubts, play blue mage on lvl 70 sync and see if you can out dps another caster.

Several things are wrong with your assessments here. Let's start with the Casters healing. Black Mage has no healing options. Summon has Phoenix every two minutes which applies a fairly insignificant regen. It's decent but nothing that will save you unless stacked. Red Mage has Vercure, which cripples its DPS if spammed and isn't potent enough to warrant. Blue Mage can adapt far better to healing because even without the Healer mimicry, it's simply better.

Which segues nicely into why Blue Mage is, indeed, overpowered. It isn't good at one singular thing. It can adapt to everything. If you watch Blue Mage vids on yotube clearing O12S, they Diamond Back every major mechanic. This completely negates what is otherwise the hardest part of Final Omega. White Wind renders any intense healing phase a joke because a DPS can become a superior healer. It's the equivalent of giving Dragoon Medica on steroids. Sure, it's a DPS loss but at 50% or higher, it's a full heal for the entire party. Simply having two Blue Mages rotating that will trivialize practically any fight.

Even if a Black Mage could, theoretically out DPS Blue Mage. It can't survive any level 70 content on its own whereas Blue Mage can even without Basic Instinct. Allowing Blue Mage into parties as a regular job, makes undeniably the best DPS out of sheer versatility.