Wut?
You don't have to "Break most of the rules of FFXIV" to make Blue Mage work.
Yes, because they wanted low effort implementation. Because they wanted Limited Jobs. Because they're afraid that anything different is somehow wrong and will be disliked by players.
And there have been numerous suggestions on how Blue Mage can have similar skill acquisition and availability to other jobs. With the extra stuff being fluff just like how base ARR classes have their own unique Hunting Logs, which aren't mandatory and haven't been replicated on any new jobs since.
Then simply don't design mandatory skills and stick them behind RNG walls
As I've mentioned, like half of BLU's current "Kit" is easy to get or just given to you directly by Whalaqee Totems.
There's no reason why the other half had to be designed as skills with low learn chances from dungeons/trials.
Then don't make BLU a hybrid. Make it a DPS like its listed as. Like it plays as (Outside some lulzy "All BLU" parties... But that doesn't make them Tanks/Healers any more than when people did all WAR runs makes WAR a Tank/Healer/DPS hybrid job...)
I'm honestly unsure which iteration of BLU that people keep referring to as a "Hybrid" since, from my memory, the notable BLU's from previous games were just basically Black Mages that had some situationally powerful damage spells and debuffs. Oh, with White Wind and Might Guard (Which was simply AoE buffs like Protect/Shell rather than a "Tank Stance") tacked on. I'm remembering stuff like Quistis, Quina, Kimahri, FFV, FFVI...
They don't really need to either. Most of the issues are insta-kill effects. Which are immuned by some enemies outside of DF as well as inside.
Cross class skills were an inherently bad design though. Since it meant that in order to play X class effectively, you also needed to level up classes A, B and C.
Which is dumb. Leveling up multiple jobs should be a choice, not mandatory to make the 1 job you want to play functional due to having key skills accessed via doing this.
Many players gave feedback about how they disliked this, which is why they removed it.
It's not at all comparable to a properly designed BLU, since it's possible to make it so that a BLU doesn't have to do anything different to other classes in order to get its mandatory skills. Especially since, all jobs have precedent for needing to complete their job quests (With its peak being during HW where every new skill came via job quest. Whereas in SB, it's merely the capstone level 70 skill locked behind the final job quest)
You can make the additional collecting non-mandatory. Thus being side content just like a Limited Job would be in its entirety, thus taking up exactly the same resources as making said content for a Limited Job would need.
Frankly this is baloney.
There's nothing about BLU that doesn't fit the paradigm of their holy trinity, outside what they explicitly designed to force BLU into this weird "Hybrid" job (At the cost of also disgracing the essence of some iconic Blue Magic spells. Like Might Guard has been a source of applying Protect and Shell (/Barrier and MBarrier) to allies in all Final Fantasy games except XI.)
What next, Red Mage has to be limited because it's (Actually) a Hybrid job in previous iterations of the game? Or could it be that there is a functional way to include a DPS job that has a heal skill (Which is literally all that BLU has traditionally been outside of XI)
Which, as noted, is not impossible to design for BLU at all.
Again, outside what they've specifically and arbitrarily decided to do with BLU (Mostly because they were being designed as a "Solo Job" and for "BLU only parties" so they made Might Guard into some BS Tank Stance), BLU is easy to fit into a clear role.
Make it supportive DPS just like how SMN currently exists. How RDM currently exists. How BRD currently exists. How DNC is very likely to exist.
Again, not particularly difficult to apply to BLU. Outside of what they specifically designed for its current state.
Again, a plethora of ways to mitigate these effects. Such as aforementioned "Duty Set" of skills. Or balancing them in a way that makes them not broken (White Wind having a CD for example, Peculiar Light being brought down to only 10% vulnerability like Contagion)
This is the crux of the matter right here.
All of the problems with BLU, have been intentionally designed.
These problems aren't inherent in BLU as a job. Not all possible iterations of BLU have core rotational skills locked behind 0.1% learn rate EX Trial bosses. Not all possible iterations of BLU have a BS Tank Stance made out of what has traditionally been an AoE team buff (Akin to the likes of Troubadour on BRD). Not all possible iteration of BLU have White Wind healing for as much as it does with no CD.
Everything that is being seen as a barrier behind BLU being a normal job, was decided to be a thing by the devs.
It's literally comparable to slashing the tyres on your car and then calling your boss up and saying that you can't make it into work because someone slashed your tyres.
Like, sure, in that example, you're stuck because your car is unusable because the tyres are slashed. But if you didn't slash them in the first place you wouldn't have that problem.
