Just gonna jump in here to back up the "Geomancer as Caster"-side of the argument. While they certainly could find a way to make Healer-GEO work, the jobs history makes it seem to me like it'd fit better into a DPS role. It's never been much of a healer before and the vast majority of iterations were more DPS/Debuffers, and I'd rather they stick with that than try to re-invent the wheel when its unnecessary.
There's also Jobs like FFTA's Elementalist which are basically offshoots of the GEO concept (and fill the same DPS/Debuffing role) that would function well to fill in any skill gaps that a purely GEO-inspired skillset would leave.
(Btw, can we all stop forgetting that classic GEO technically had access to all elements through different Terrain/Weather and would thus be a prime candidate for a true elemental caster? Sure, FFXIV's version points out Earth/Wind/Water specifically, but seeing as Ishgardian Astrologians are very different from the AST we got I dont see that as an issue :P)
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Technically off topic but:
Forgive my bluntness, but this is nonsense. Right now most encounters in the game have healing requirements that are so low that they can be met through OGCDs alone while full time DPSing, which is a big part of why healing is so boring atm. And even the encounters with harder requirements tend to have a lot of healing downtime, spending a few more GCDs on actual healing would at best provide more variety rather then cause any mechanical problems.
We're playing a game where Damage (especially partywide damage) is mostly coming in predictable spikes, and due to that fact all that would really need to be done to shift to a more GCD-focused healing design is reduce the overall number of oGCDs. OGCDs don't need to go away ofc, they just need to be more a limited resource rather then the main focus of the healing kits as they are now.
There is nothing that needs to change about encounter design, healing predictable damage per GCDs instead of using an oGCD while full time DPSing wouldn't change much, if anything, really.
Healer-DPS doesn't need to be adjusted past making up whatever is lost through adjusting whatever skills are already there or adding back skills previously removed or (obviously) new skills, possibly of a similar fashion as WHMs Afflatus Misery (i.e. skills that reimburse the caster for using GCDs on healing).
What gets often lost in these healing conversations is that prior to SB healing was a mostly GCD-focused endeavor, and even in Stormblood healing was a lot more balanced between GCDs and oGCDs, and the game functioned perfectly fine. Shadowbringers really didn't change enough (if anything) about encounter design to warrant as many oGCDs either, so I don't see how a shift back to a slightly more GCD-focused system would cause issues.
It's also important to note that SE seems perfectly willing to change whatever few encounter would "break" due to role changes (which would likely only affect Ultimates anyway), given that that's exactly what they did at the start of ShB to account for the Tank changes.