BLM is fine. Melee are fine.
If anything, melee are arguably more meta than ranged because of how damned hard it is to kill them in team fights. All melee have some means of self-sustain beyond the expected potions, and these are available more often/are more potent than typical caster/ranged defensives (SMN is the only exception here, being quite possibly the strongest buff in the entire game.) And, obviously, they have a lot more HP.
SAM: Meikyo cleanses a debuff, Chiten is 25% DR and 2000 thorns damage for 5/30 sec, Ogi procs an 8k shield when used for AOE, and Oka is a 5k AOE that has 100% leech.
DRG: Horrid Roar is effectively 50% DR for 10/30 sec on targets affected, Chaotic Spring is 8k with 100% leech, LB generates a shield equal to 25% HP, and Elusive Jump cleanses two types of debuff and grants sprint. They are generally the most twiggy melee, but Horrid Roar is the most effective "DR" in the game while it's active. Probably the highest skill floor in terms of "don't die like a chump" among melee.
RPR: Crest produces a 12k shield and then produces a 6k*2 Regen effect in an AOE after the shield is consumed, on a 20 sec cooldown. Harvest Moon is a 4-8k hit with 100% leech.
MNK: Riddle of Earth is like a personal Macrocosmos (though doesn't automatically pop like Macro does, for some incredibly stupid reason), and produces a 6k shield on themselves any time they dash to an enemy (3 charges/10 sec.)
NIN: NIN is probably the most durable non-PLD in the game. Probably *more* durable than PLD if we count their ability to evade attacks on top of their skills. But for reference, Shukuchi is a teleport on 15 sec cd, Huton is a 16k shield plus sprint on a 15 sec charge, and Meisui is an 8k heal plus 4k*5 regen.
Casters and ranged, on the other hand, typically get a single defensive skill and that's it. You'll notice that all of the melee have at least one core defensive skill and then typically a life leech skill (Riddle of Earth is basically MNK's leech skill), on top of their higher HP. Melee are pretty chufty.
They also generally have a good mix of DPS and CC. All-melee teams can absolutely obliterate ranged-heavy teams simply by virtue of out-tanking the damage and bursting the much flimsier casters down. Think about how much less effective ranged and casters are when they have a melee stuck to them. Ranged only have the advantage on the *approach.* But if an entire team initiates together and intelligently, you can mitigate that advantage substantially.