The point of Blue Mage is to be overpowered. That was its original design intent in FFV.
It was originally a job that relied on meta knowledge with its first skill learned being called, "Learning."
If you know how early you can acquire all BLU spells in FFV, then you can basically be Fantasy Batman and pull anything out of your utility belt and one shot or trivialize all of the game with it.
For instance, in Galuf's final fight against Exdeath, if you are sufficiently leveled(40~50ish) and using a BLU build with every spell acquirable up to that point, it is actually possible for Galuf to never be reduced to 0 HP. This is not possible on any other job at an equal level, afaik.
In FFVI the canonical Blue Mage is Strago, and the same thing goes for him as it does for BLU in FFV. If you know exactly where to get Blue Spells asap and know exactly how to employ them, then he can be OP busted without ever learning spells from Magicite. Of course, since Magicite and general magic are already OP in VI, you actually have to go out of your way to do that.
The non-canonical Blue Mage in FFVI is Gau, because while his skill isn't dubbed blue magic, it's functionally the same albeit in a berserk state once you select the monster skill set he will use. If you know which monster sets are OP early, then you know which monsters to hunt for on The Veldt, and then you can get things like Gau using General Leo's Shock or Gau casting Tier 3 black magic for free endlessly. Or shooting lasers out of his face. Or missiles out of his eyes.
Then we have the Enemy Skill materia in FFVII because FFVII characters aren't allowed to have unique skills outside of limit breaks... If you can get the Enemy Skill magic Beta from Midgar Zolom, then it will trivialize like the entire first two discs.
Quistis only uses Blue Magic via Limit Break so... meh (don't get me wrong I LOVE HER).
Quina is back to Blue Mage roots with being absurdly OP for all the same reasons mentioned above. Something something, level 1 Ozma kill?
Khimarhi goes the jack of all trades route and is like half dragoon. I'm not aware if he can get OP as those mentioned above, but everything I'm aware of says nah fam.
Then we come to the glorious FFXI Blue Mage... but is it really so glorious? Well, about that...
Blue Mage was not available in FFXI until 2006's Treasures of Aht Urhgan expansion. It took the game by storm due to introducing spells that couldn't be bought and also required no questing. This meant they had to be gained through combat alone, and you simply had to see the spell get used on a target you had enmity on. The higher level the target, the easier the spell was to be learned, something a lot of people never picked up on, preferring to AFK against Too Weak to Be Worthwhile monsters and watch cat videos and flash cartoons on AlbinoBlackSheep.
Many of its spells were physical and quick to cast, meaning Blue Mage could be very very active even very early, and it could often kill monsters rated Even Match to Very Tough depending on monster type and spell advantages. As it leveled it first gained the ability Burst Affinity, allowing it to make its magical damage Blue spells Magic Burst like Black Magic ( they can't without the JA). Then a little later it gained Chain Affinity, allowing it to skillchain and SELF skillchain with its own spells and weaponskills. So it became a job that could do Party Mechanic of Skillchain > Magic Burst by itself from level 40 onward.
Keeping in line with its history it was allowed to use swords as a call back to FFV, and in FFXI they flavored it to used curved swords. This meant that Blue Mage in FFXI had relatively high melee damage capability outside of its magic, and was more or less as good at melee as some of the melee jobs when their JAs were down. Combine in its spells, and it was a real great damage dealer until it ran out of MP.
This put it in awkward straits for the middle level ranges in parties that didn't want to wait on DD MP. Or even refresh a non-healer. So a lot of Blue Mages took up the Black Mage leveling options at the time of targeting beastmaster beastmen's pets. These pets would be the same level as the beastmaster, but have significantly lower HP, so they could be killed within a few spells. While not ideal, this meant that Blue Mage could actively level while still having a decent chance at getting a party invite. Once it was in the 70s, provided it had the spells, it could solo Imps in Caedarva Mire and many Blue Mages of that day would solo Imps to about Chain 2 or 3 instead of joining parties at all for both leveling and meriting.
So then, how did it fare in Endgame? Well, not so well. It wasn't considered meta, though it had several options to deal consistent, solid damage, even at range. Its biggest claim to fame at the time was the spell Cannonball, which has a 24' or so range and also stacks with the THF job ability, Sneak Attack, while also having its damage be modified by Defense. This combo could be used to hit HNMs for big numbers or while they were being kited, and it also allowed BLU to do things like Zombie the Pandemonium Warden to keep it from Regening. (Zombie-ing being getting a raise and then attacking the monster over and over, the excessive range of Cannonball letting them keep it claimed longer and reclaim it from far away).
Many of its best spells came from areas locked behind Chains of Promathia quest progression, which at that time was still level capped, so many BLUs never got their whole spell repertoire when the job was new.
However, as the years went on, with the level cap increases, BLU would get new spells each time. And each time these spells would be rebalanced in favor of the higher levels. BLU burgeoned in power, and then when the level cap became 99 there was a big question as to whether or not it would keep getting new spells. Iirc, towards the start of Seekers of Adoulin, SE said they would give BLU one set of Adoulin spells but that would be it. But as it turns out, that was partially a lie, and BLU got more new spells even after that Adoulin set, though most of those spells would fall under the, "Unbridled Learning" category, a category of spells requiring the use of a JA by that name, considered to be so powerful the option to cast them had to be gated by a JA.
Then for a time, BLU was the most powerful job in the game because it had access to everything. Capped magical haste by itself with Erratic Flutter and Mighty Guard. Power physical WSes, powerful magic builds, and powerful AOEs even. It still has all of this today, but some changes to the way certain monsters and spells work, and it has somewhat been whipped back into line. Sort of.
This brings us to FFXIV's rendition.
They said right out of the gate, that they wanted Blue Mage to have its iconic instant death and doom type spells, as well as its enfeebling and other things that don't all have a place in XIV's trinity system. They didn't want to pin Blue Mage to a distinct role, because it can do it all!
It's very possible that they could have made it a caster that learns it spells via job quests that target specific monsters or memories. But they did not want to compromise its original vision. This OP superhero.
There is no having that vision in a game that demands tight balance. Where people get upset if one DPS is leagues ahead of another. Leagues being like 4%.
Yet this is also a game where the best combat content is in the raids and trials, and most of those require more than one person to perform their mechanics. The achievements are there to entice you to do it. All of these raids are actually incredibly easy on BLU. BLU is so powerful it can outright skip so so so so so so so SOOOOOOOOOOOOOO many of the mechanics of old fights. Particularly now. Though there are some notable exceptions if you're trying to bleeding edge them. (Like it couldn't skip Gavel in A8S until Stormblood spell line)