They have historically had and even now have less non-rDPS utility than certain jobs that are not Physical Ranged, and haven't uniquely had access even to granting TP since 2.4 or MP since 3.0, so that connection was largely a misnomer then and is vestigial at best now.
And if you fixate the whole of the Physical Ranged role greatly around ally-dependent indirect value then you effectively remove the option to play with any of those aesthetics (bows, guns, etc.) unless one's into that degree of support (as opposed to personal carry potential / direct value, etc.).
So, again, no, I don't think the whole of ANY role should be turned into Support, nor do I think that label should siphon off jobs piecemeal (NIN, DNC, RDM, etc.) into a new Role.
Imo, the best course is to just avoid that separate label for a 'supportive' job entirely (it's nebulous af, as it ignores the actual primary function of the job as is essential to matchmaking) --regardless of whether that label be "Support", "Physical Ranged", "Ranger", or "Thundercat"-- and just allow what jobs would fittingly want more support options... more support options, regardless of their role.
Rather than altering any role wholesale or sectioning off a bunch of jobs via a tangential description irrelevant to matchmaking like "Support" or "supportive", just give RDM additional utility but at-cost (rather than pre-taxing it for merely having that ["free"] utility), reinvigorate Bard's songs to optionally provide utility (again, at-cost in some way), let Dancer be a bit more Dancer-y while allowing it more personal throughput (still almost always a net loss) when Closed Position isn't active, and allow SMN more indirect value that can be milked from its summons (again, at least slightly at cost), etc.
At this point, the only Full Party matchmaking criteria should be 2 Tanks, 4 DPS (at least 1 Melee and at least 1 Ranged so both ST and AoE LBs are accessible), and 2 Healers.
There is functionally no difference between Physical and Magical Ranged dps that isn't already overshadowed by the differences just between Red Mage and Black Mage.