I suspect SE actually did consider having a support role in the game at an early stage as early Alpha images publically released officially by SE show ARC's class logo in yellow not the 'DPS role' colour of red that it has in the final game, so whether that was to denote a 'support' role or 'ranged DPS' role is unclear. Either way, at some point they probably decided it was better and easier to just maintain the 'trinity' and scrapped that idea (hell, even earlier mock-ups for the game just recycled 1.0's style of Job icons where the Job icon's colour was whatever colour their Soul Crystal was), and thus from the Beta test into actual launch ARC's logo is in red denoting 'DPS'.

The problem with support type roles is they usually end up being rolled into another role anyway and so it was perhaps easier on SE's part to just have classes and Jobs that are technically support as 'DPS' or 'healer'. FFXI was a very good example of showing how this normally ends up: certain Jobs were meant to be such 'support' roles but usually also had to function more often in different roles based on their abilities - RDM, COR and BRD not only buffing but also serving as 'mana batteries' for healers and, in RDM's case at least, healing too. COR and BRD were also more often invited into parties simply for their abilities that boosted EXP gained which, back in the old days at least where EXP for each enemy killed was miniscule and so players had to try and wring every last EXP out of a fight any way they could, this was only natural. Making them more just EXP amplifiers.

Something that is not needed here in FFXIV with EXP pretty much freely given away like candy and FFXI style EXP parties being well.... non existant.