The issue is even despite these inherent weaknesses, Melee still beat the Range in fights where they are heavily disadvantaged. In fact, lets look at E6S—arguably the most unfriendly melee fight in years.
Summoner - 16,911
Black Mage - 16,575
Ninja - 16,325
Samurai - 16,214
Red Mage - 16,005
Monk - 15,950
Dragoon - 15,917
Machinist - 15,857
Dancer - 15,422
Bard - 14,970
That is the spread at 95%. Bear in mind, Monk and, especially Dragoon, have no way to mitigate disengagement. Meditation is meager compensation for a GCD loss and Piercing Talon is so laughably weak, it's actually better for a Dragoon to do absolutely nothing in most cases. So a Dragoon literally not attacking at several points does more damage than an optimized Machinist, Bard or Dancer. Bard, in particular, is so far behind in E6S, it's bordering on useless. We could somewhat justify this if utility such as Refresh, Foe's and the like still existed. Instead, Range "support" is Troubadour and friends. Are they really so much better than Feint to justify such a massive difference?
Now lets look at E7S, where Melee downtime is basically non-existent. Dragoon jumps to over 1,400 more rDPS than Dancer; 1,100 over Bard, and 800 over Machinist. Meanwhile, you'll notice the Casters have essentially zero issues regardless of the fight design. If positionals and uptime are going to be an excuse then Melee should deal the highest damage since they stand to lose the most. That isn't the case as no matter the encounter, Summoner is significantly ahead all but Samurai.