I think the two biggest issues with drg right now are not enough damage, especially when considering the effort you need to put in compared to something like reaper, which se apparently wants to balance around, and the complete lack of a defensive skill, all other melees have something, with the currently 2 best dps (monk and reaper) also having some impact for the rest of the party members.

I think the damage issue is the most pressing one, as dragoon is one of the jobs currently being filtered out by the harshest dps check in the game, p4 savage, meaning it gets dropped the moment dps is actually required.
If you look at the number of parses, drg is in the bottom 3 together with ninja and dancer for both bosses in p4, meaning that players clearing it mostly agree it is a suboptimal choice that is going to artificially make the fight harder for them :
https://www.fflogs.com/zone/statistics/44#boss=81
https://www.fflogs.com/zone/statistics/44#boss=82
Yes, obviously the job is still able to clear, but when it comes to challenging content, the path of least resistance is always the most attractive, and the fact that any player that got to p4s as drg can switch to reaper and perform better with less effort is just not good for the game. It should also be the relatively easier issue to fix, the 6.05 changes were in a good direction but just not enough, maybe try and be less conservative with buffs if nerfs to top performers are not going to happen.

The lack of a defensive skill is the other big issue in my opinion, life surge in theory heals you a tiny bit, but its such a small percentage, plus you are kind of forced to use it for damage, honestly having 2 charges of this also feels kinda bad, its not an exciting button to press, if its going to stay as it is id suggest making it a guaranteed critical direct hit on the next skill, so at least it gives the dopamine rush of the !!! numbers, its just filler otherwise. I personally would prefer if this became a different purely defensive skill and the potency it gave was baked into heaven's thrust to compensate. Whatever the case it feels bad to be the only melee without at least some way to help mitigate damage, if this is on purpose for class flavour reason there should be some upside somewhere else, i dont think its good flavour if its just one job not getting access to something.