Most statics would do this, because this has been the trend we've seen already in SB and HW.
Most players want this. I run tank predominately and of the 2000+ dungeon/trial content, I can only think of a small handful of times when party members wanted to take time doing it. The most common thing is "Pull big and pull hard to get this done." and if I dont do it, someone in party will insist. So player tendency is generally get things done fast. BLUs with their skill sets will be where thats at. It seems you understand that BLU is gonna cause problems with how DF/PF work given their skill sets.
This would probably be the best direction to go to allow BLU have more content access, but Im sure you would agree that the immediate knee jerk reaction would be "It's not really a full class/BLU is being punished". It undermines what youre trying to do. It will still be limited.
Yes, this would be semi functional, where youd use a rotation to build up resources to use BLU skills. My immediate thought though is this seems a bit to thematically similar to RDM, even if its inversed. RMD Does the hybrid caster/melee thing, SMN has pets, and BLM is glass cannon magic man. Having blue use both melee/caster would kind of overlap with RDM in a thematic sense. This wouldnt be inherently bad but it would raise some quizzical eyebrows. The only issue then is role selection issues. How would this function for healer particularly.
The issues then, since were talking about learned skills in a DF or PF environment, comes down a few things. For one, how many skills do you need to bring a BLU into a dungeon? You would have to enforce a minimum. Then it comes down to which skills can and cant be learned/used. For example, technically you can learn about any skill currently as long as you meet the basics of seeing the enemy die and tagging it and not being dead. Not impossible, but you could get mountain buster at lvl 10 with an undersized party. So having a BLU come into a low level dungeon via DF but having Mountain Buster (or similar) is a balance issue. Not game breaking, but annoying enough. The only current solution I can see that is viable is skills have a gauge cost, and the stronger skills eat more of the gauge. For example, you could learn Mountain buster at lvl 1, but if it takes 60 energy, and your gauge has a max of 30 at that level, there is no point in learning it other than getting it out of the way. In synced content, gauge would sync down to appropriate level to prevent certain skills. As for skills needed, a tier system would need to be implemented - you need 15 skills to queue for dungeons between lvl 15-20. 20 Skills for 20-30, 25 for 30-40...etc. This way you need a bare minimum of abilities so you cant go in without skills.
Beyond that youd need to set up skill into 4 categories: Defense(Tank), Restoration(Heals), Offense(DPS), and Neutral (all aspects). Remove aetherial mimicry from the game and provide stances instead that you learn as you level of. Each stance grants a bonus that would operate on +5% more damage, or +10% Defense/HP, etc, but in activating these stances, You lose access to all off categories save the neutral aspected stuff which can be used universally. If you do decide not to use any stance, you have access to the full kit but wont be able to use DF cause you cant fulfill a role.
The final thing still ends up being that certain skills are just that detrimentally strong that they would have to be nerfed. I gave it thought regarding some of this, and the thing that would have to be done to mitigate against this would be debuff the boss twice, so that lets say you use Off Guard, the boss gets a buff or bonus that prevents the reapplication of it for 60 seconds. It isnt perfect but that would help fix atleast one spell. Beyond that, youd still have to figure out how final sting works among other things (create special resistances to it possibly where the boss actively mitigates against these kind of attacks as to make them not worth while overall, or make it a specialized execute that is only useable below 5% hp or something). The other way is just redesigning how final sting operates, where rather than killing you, it just reduces HP to 1 and has a looooong CD on it. But these are two examples that would need to be addressed, and if you want BLU to flex and be any role, there is a ton of work that needs to be done in regards to how tank and healer roles are.
And while the suggestions I provided might work, I want to remind you that these kind of things would require rebuilding the class from the ground up. This isnt something I think the Devs are interested in doing.