It is entirely possible to make Blue Mage a full job while retaining all of its current identity. I know this is a wall, but please consider this.
Firstly:
We need to create spell list #6 which is strictly for group play (you cannot enter the Masked Carnivale with spell list #6 equipped).
Some spells will either need to be forbidden from being set, or will need to have their effect altered (which is already a system implemented in game via AST sects and ACN summons). One example of this could be making Level 5 Petrify apply an additional effect (like a DoT) whilst it is set in slot #6. This way it doesn't interfere with its combo with Drill Cannon and still serves a purpose.
Relevent enemies (even at 50) already have immunities to most of BLU's effects like petrify and paralyze as it is. Spells that paralyze and petrify can actually keep their effects, for the most part. They are functionally no different from a WHM Holy stunning trash packs, a BLM sleeping groups in low level dungeons, or a PLD pacifying a boss, and already feature diminishing returns. If absolutely needed: if an enemy is immune to Sleep, make it immune to paralyze (seems to be the case with bosses already); if an enemy is immune to stun, make them immune to petrify. It should also be noted that various potencies would also need to be altered if set in spell list #6.
- Set #6 will only work if it has a total amount of potency, or power. If you don't meet X amount of power, you can't queue; it would function just like any other check, like item level. This should be a range, however, with a minimum acceptable value as well as a maximum value.
- If you only meet the minimum power requirement, it will be due to having several support skills equipped. This minimum power should be roughly equal to RDM in DPS.
- If you hit the maximum power limit, it will be due to having no support skills equipped. This maximum power should be roughly equal to BLM in DPS.
Since we are limited to only setting 24 skills as it is, it should be very easy to balance when using a range-of-power system. It would even echo FFXI's system of each spell being worth so many points - with more powerful spells equating to be worth more points.
With the nature of spells that BLU gets in this iteration, it wouldn't likely be very cookie-cutter, either. You'll have some BLUs that prefer to focus on some support via spells like Ink Jet, Bad Breath and White Wind who pull the DPS of a RDM; you'll have some BLUs that prefer to go all out with damaging spells who pull the DPS of a BLM; you'll have some BLUs that fall somewhere in the middle pulling the DPS of a SMN. There may be some favored spells, like Peculiar Light, but that can/should be kept to a minimum by various methods.
Secondly:
We need to take a look at their gameplay. As it is, you pick your best potency spell and spam it. Spell list #6 should increase the recast on most, if not all, spells by quite a lot. However, with each cast of a blue magic spell, their spells on cooldown would have their cooldown reduced by a certain amount. Think of this in a way similar to Scholar's Aetherflow cooldown being made shorter with each use of an Aetherflow ability. This would prevent the overuse and misuse of abilities like White Wind and would be used to set up strategic abilities like Bad Breath (for its mitigation effect).
This not only sets up the BLU to choose the spells that they bring into battle, but also the order in which they use them (aside from spells with set combos (e.g. Aqua Breath > High Voltage)). You could play BLU as a long-range caster exclusively, a short-range caster exclusively, or even mix it up with both types similar to RDM if you wish due to spells like Flying Frenzy and Loom. You could focus purely on magical damage, purely on physical damage, or mix it up with a bit of both, especially should you be paired with a RDM who actually buff BLU's physical spells.
Thirdly:
An importtant thing to consider is the ability to make BLU a caster-based tank due to Mighty Guard. Setting Mighty Guard in spell list #6 could force a role-change and turn BLU into a tank. Some spells could be made to bypass the reduced damage while set in list #6 (e.g. breath and/or Primal spells), or be altered to feature a bypass for the damage reduction (e.g. Moon Flute) in a similar way that Warriors can do. Mighty Guard could feature additional passive effects while active to even out the tanking playing field, including HP and defense increases, inability to have casting interrupted etc. Diamondback and White Wind are already the perfect emergency buttons and the above gameplay idea would limit their usage/spammability.
The main problem with this however is that BLU tank would be very cookie-cutter. There are many abilities that would be required; Ice Spikes, Veil of the Whorl, and all of the aforementioned spells would be expected. The only spells that wouldn't be subject to this would be whatever is leftover for your DPS/combo choices. However, even with that, it may be better to feature a complete tank spell set list (list #7). This unfortunately would be very limiting but more easily balanced with other tanks; this would be a small sacrifice to make, though, when looking at the larger picture of giving BLU not only spell options but role options.
In closing:
I would never expect such a change to be rolled out all at once. I would never expect it to take priority over adding new content. I would like BLU to maintain its presence in the Masked Carnivale with future trials and to be able to run amok in the overworld and undersized parties with their spell sets 1 thru 5 at full power. I would like BLU's full power and the Masked Carnivale to be but one extension of the job, as playing songs in towns is an extension of BRD. I just wish for a job that has so much limited, to have the chance at being closer to unlimited.
* I fully give permission for any of my written ideas to be used by SE without accreditation.