We have "Support" but you wouldn't call it that because it doesn't even look like one. Healers are supposed to be "Support" but they can barely support outside of just healing/shielding. They're just 1-button DPS otherwise, and it sucks on so many levels.
AoE Esuna? Removed. Increased Skill speed & Spell speed? Removed. Restoring TP? Removed. Regenerate MP to party member? Removed. Knockback enemy? Removed and replaced with Bind. Where's Bind you ask? Removed.
Pretty much all semblance of support has been reduced to just DPS for the sake of balance and 'ease of use without stress on that party member to make a difference whether the party lives or wipes'.
Literally, the ONE support skill that isn't just a DPS buff is Expedient because it gave movement speed in combat, and that's only unlocked on SCH at level 90 and usable every 2 minutes. And even then, the movement speed effect got nerfed.
The one actual support skill all healers have is Rescue - the skill that so many players complain about. People don't use it much because every job has so much mobility, because it has a huge cooldown, and because of the pull delay that it's easier to make a mistake from using it. Not to mention, a lot of mechanics outright don't even allow the possibility of rescue from messing up a mechanic. You can't rescue someone from Down From the Count debuff (Holminister Switch Left/Right Knockout, P5 Devour), can't rescue a target that's chained to move them (Holminister Switch Chain Down, Battle in the Big Keep Enchain, Kugane Ohashi Hell's Gate), Can't rescue someone that's about to die from being eaten (World of Darkness Stepping into Slabber and being stuck). The skill has so many limitations to its usability. You only use it if you are sure you can pull someone to safety or to pull someone mid-LB animation to safety. Otherwise, you get blamed even if that person was going to die otherwise because you "interrupted them".
Ranged DPS are supposed to be "Support" but most of their support utility is just DPS, but you can literally count the number of support utility they provide. They have bind, heavy, and interrupt skills, but they rarely see usage. Peloton gets usage but mainly in dungeons and alliance raids, not in combat. Their individual shield mitigation? That's basically Feint/Addle, but applied to parties instead of a target. We have Warden's Paean, which is just a longer-lasting Esuna effect.
MCH? Is that even a support? Maybe during Heavensward, but not anymore. It's hard to call Physical Ranged DPS as the support class when MCH doesn't support the party outside of Tactician. Even MNK can be looked like a better support class than MCH (provides a DPS buff to the party, an AoE healing up buff, and Feint).
Physical range DPS is not so much of a support role because it has support utility, but because it supports the party by attacking from afar... which isn't even true anymore due to boss hitboxes getting big enough for melee uptime.