Which fight are you talking about? Seriously, if you are a fire mage, you can definitely compete with the melee, and probably out dps most of them too.
There are tons of fight mechanics that screw over melee in the current raid
Morchok - range can still dps while the blood is out, other than rogues who can stay in the blood, the other melee are screwed (mages 2nd on charts only after rogues)
Yorsahj - melee has to run really far to adds (mages on top)
Zonozz - normal is fair game for everyone, range is preferred on heroic to be able to kill adds without wasting time on travel, melee gets screwed on adds, and is only competitive here if they are allowed to stay on the boss + cleave adds
Hagara - melee is fucked on the frost phases, while range gets to stand still and dps through the whole thing (mages on top again)
Ultra - fair game (mages still on top)
Warmaster - casters on top, rogues not being far behind due to cleave
Spine - mages famously being the best on heroic
Madness - tons of stuff to screw both melee and casters, but casters are on top of the charts on here as well
For H. Morchok everyone is fairly even, but I waste DPS time because our group setup ensures that I die if I don't juggle armors for stomps. This is specific to my raid of course, but the "dps during blood" bit is pretty unreliable/overrated as the blood is buggy as hell on heroic. I get 3 fireballs in at most, occasionally I have to outrange my spells to not die.
For H. Yorsahj melee stays on boss and doesn't have to scorch during blue phases. (We do this correctly... i.e. we save balls at low health and pop them immediately, but I still run into mana problems and occasionally juggle armors so I have mana to AOE plus some mitigation.)
For H. Zonozz whoever is stuck on boss the whole fight is 30k ahead of anyone else. It's a meters-are-irrelevant fight in the same vein as Alysrazor.
Hagara is pretty even. I lose to melee probably from moving around to intercept ice lances plus lack of decent, on-demand AOE for ice tombs. But our melee were 4-8k above our top ranged on our last kill.
Ultraxion is the closest thing to a patchwork... winning or losing that is down to crit lottery.
Warlord seems pretty heavily melee favored as they don't have to move around and can cleave the shit out of adds. Our melee were 40k and 35k respectively on our last kill and all of our ranged were even at 21k.
Spine favors arcane more than fire even outside of heroic so this is somewhat my fault, but tons of little adds that die quickly isn't a great situation for anyone with a cast bar... plus ranged has wasted DPS time switching to corruptions for grip. On our last kill melee were both 5-6k ahead of ranged.
On our last Madness kill both melee were ahead of my 49k DPS by 3k and 6k respectively. I think part of it is that they don't have to single target tentacles, but it could just be that multi dotting is a fail strat as fire on that fight and my globals are better served nuking with the haste and damage buffs.
Anyway I'm mostly going off what I observe in our own meters. It could just be that our melee is better geared or that I'm a fail player but given that our melee and ranged are clumped together in two distinct sections of the dps chart I think it's a trend of the instance.
Another possibility is that the melee AOE trinket and mind flay tentacle sword make warriors overpowered as hell.