I think there are two things going on here.
First, a lot of the "problems" (term used loosely) are, IMO, tied to retaining the class terminology post armory overhaul. "Gladiator", as a fancy translation of "sword user", was OK when the original classes and armory was the end of the discussion, but it doesn't really fit with the new system, where the original class decision is a more generic, solo-friendly, role. The "gladiator" is able to solo by virtue of absorbing a lot of damage (i.e. tank) while putting out decent damage vs. the more balanced attack/defense of the "pugilist" or the more nuke heavy but defense light "thaumaturge". Had the classes gotten renamed we wouldn't be in the mess we're in with Barchers (or Gladins or Punks or whatnot).
If we had:
Close Damage dealer -> Monk
Standard Damage dealer -> WAR
Mid-ranged Damage dealer -> DRG
Long-range Damage dealer -> BLM
Support -> Bard
Healer -> WHM
Tank -> PLD
nobody would blink at the "transition" to the new titles and roles. The problem is we have the defined original titles with what should be more generic roles - which is a disconnect.
I think Yoshida has done a terrific job turning FFXIV around, but the decision to retain the armoury system, and the 1:1 ratio of weapon to class and then the 1:1 ration of class to job, is inflexible, which is precisely what the original concept of the system was trying to avoid.
This problem of perception could also be dealt with by not having the 1:1 class:job ratio. But if the ratio persists, the original class names should have been made generic.
The second issue is seen easily from the above list I think - that Archer was not originally a support job - meaning people who selected archers did not want to play that role. If the party role for the archer is support, you've "forced" (as much as it can be forced, which it really isn't) archers to play a role they didn't want to play. This argument could also be made for some of the other classes, but it is more pronounced with an Archer/Bard line than a Gladiator/Paladin line.
Ideally, given where the game is and where the development is, what I would like to see is a full move away from 1:1 class:job ratio. That would probably be the least disruptive. Hit level 30 and you can unlock whatever extra "party-focused" job you want.
Even if some (or even many) of the skills of the job have prerequisites from a particular class, so be it. Assume that 50% of the Bard skills require some prerequisite from Archer alone - that's ok. That might essentially require some playing of archer to unlock all of the bard skills, but it doesn't put them on the same linear path.
Anyway. Enough rambling...