A simple example:
Suppose a Barrier healer had one 10% damage reduction ability, a 100 potency (let's say worth 100 HP) shield, and a 200 potency heal. This means that in terms of effective HPS, if they have a party member with 100 HP and a tank doing an attack of 100 HP, their party member will survive with the mitigation (taking only 90 HP worth of damage) and their 100 shield placed can also protect the party member (eating all the damage), and if they use both, the party member will be at 100% health with a further 10 HP shield. On average over a given fight using these abilities, the Barrier healer here will effectively provide a total of 300 potency worth of healing between the heal and the shield (assuming shields are 100% used up), and by mitigating damage by 10%, this makes an effective x1.1 to their healing (or something akin to that, might be 1.09, but same ballpark). This means they are, on average, providing 330 healing, and party members will not die to a hit of anything less than 190 HP since they can shield and mitigate it, and then 200 heal immediately after it with their direct healing spell. Note this also works if you flip the heal/shield portion to be a 100 heal with 200 shield.
Now, suppose a Pure healer has no damage reduction ability and just a 300 potency (let's say worth 300 HP) heal. Their party members must always have more HP than the attack in order to survive it. Their HP pools must be bigger than any unavoidable raidwide (not always true in minilevel gear). Assuming they are, boss hits must consistently strike for 300 for this healer to not be overhealing, and even if they did, the Barrier healer described above does 330 effective healing anyway. So this healer is only useful when there is consistent high damage, and its heal must be tuned to be 330 or greater (say 400) before it actually is appreciably more useful in that role than the Barrier healer. And that's ignoring things like Pepsis exist.
Granted, our healing kits are far more complex, but the example shows that mitigation makes up for raw healing in terms of effective HP [eHP] and that enemies need to reliably out damage that WITHOUT one-shoting party members AND the Pure healer needs to have a greater combined total healing potency than the Barrier healer's (heal + shields) x mitigation multiplier.
In live, a SGE can output NEARLY the healing numbers of a WHM absent Cure 3 spam. At its worst, Ixochole is as powerful a heal as Assize and up more often, Kerachole is approximately equal to Asylum and up more often (shorter duration but can be reapplied 3x per every one Asylum), augmenting that with Physis creates ROUGHLY as much healing over time as a WHM maintaining Medica 2 consistent uptime, Eukrasia Diagnosis (when it doesn't crit) is 300 potency of heal + 540 potency of shield = 840 vs Cure 2's 800 potency and Pepsis can not only turn that shield into a 450 potency cure but can do so every 30 seconds AND can do so even 1 potency/1 HP point of the shield is remaining, meaning this could be as much as a 1,239 potency heal. Holos matches Temperance pretty well with yet another barrier, Panhaima matches Lilybell with a shorter CD, standard Prognosis (300) is 3/4ths of a Medica (400) at 8/9ths (800 MP vs 900 MP) the cost, with the Eukrasia version is a 100 cure + 320 shield, for 1.05x a Medica (420 vs 400) at the same 900 MP cost, and can be Pepsi converted into a further 350 potency heal, making it up to 769 potency AOE, which is nearly twice a Medica's power. Medica CAN be buffed by Plenary, but only once per minute (instead of Pepsi twice) and only gains 200 Cure potency per Medica, making it 600 vs up to 769.
Solace and Rapture are Cure 2 and Medica that are instant and MP free, but gated by only once per 20 seconds. They ARE damage neutral, but SGE is also getting 170 potency of healing every damage spell cast, meaning every 3 Dosis (510) is effectively casting Cure 1 (500) on a target with no DPS loss; every 5 is 850 potency, or greater than a Cure 2 (note Cure 2 costs 1,000 MP to cast). And this is all free healing with Kardia being swappable every 5 seconds.
And I'm not 100% on the math, but I think SCH makes this even more absurd.
Point is, the Barrier healers have as much, comparable, or more healing than the Pure healers do. Further, their mitigation not only makes this healing more useful (eHP multiplier), but also allows parties to survive what would kill them. For the Pure/Barrier split to even make sense, Pure healers would need to not only outheal the Barrier healers, but do so by a fair margin. That is, for every 100 HP a SGE can heal, due to the eHP multiplier, a WHM needs to heal 110 HP just to be even with it.
ALTERNATIVELY, the Pure healers could be more efficient. Sure, Medica 1 and Eukrasia Prognosis may be comparable in healing, but if Medica 1 cost 500 MP, then WHM would clearly have the upper hand in MP management and sustain/spam healing...but it doesn't. With the Thin Air nerf in particular removing the Cure 3 spam option, which is what WHM had over SCH and AST in ShB. Not only that, but SGE has better MP and even gets refunded MP by using its oGCD heals, encouraging their use. For this version of the paradigm to work, it would need to be WHM and AST that have the MP efficient heals and better MP management, and SCH/SGE oGCD mitigation tools and shields would all need to have MP costs and be MP expensive so that their use had to be carefully monitored.
As it is right now, SGE can cast 2 Kerachole's per minute offering 10% mitigation to the party, 500 potency worth of 100 potency per 3 sec HoT ticks, and it even refunds the SGE 7% of its MP. This is 1,100 eHP potency and 14% MP regen. Conversely, WHM casting Medica 2 2x a minute is 500 potency of cure and 150 x 10 potency of HoT, or 1,300 total potency (but lacking the "damage mitigation saves lives from being one-shot), and COSTS 2,000 MP or 20% of the WHM's MP pool. While it's true the WHM can do this 4 times, doubling these numbers, it also doubles the cost. 40% of the WHM's MP would be comsumed doing this, as well as 4 GCDs, while SGE is generating + 1,400 MP and able to do 1,350 potency of Dosis damage and generate 680 potency (basically a Tetra's) worth of healing on their Kardia target in the process.
And this comparison holds looking across most of SGE vs WHM's toolkit (note I'm not bringing up SCH because it has more or less the same toolkit as SGE with a few extras AND a party damage boost from Chain Strat; but basically the comparison with SGE is "Same thing, but even more.") Barrier healers have comparable healing to Pure healers but also bring additional mitigation and HP buffer shielding to the table. And because of how more useful percent mitigation is alone (ignoring shields) Pure healers have to be able to do a lot more outright healing, and it needs to be more efficient, to make up for this.
AST KIND of escapes from this because it has a 400 Potency shield every 30 seconds from Celestial Intersection while matching WHM's one party mitigation with Collective Unconscious which is available twice as often as Temperance is, and still has Exaltation to match Aquaveil.
The game has two Barrier healers, one Semi-Barrier healer (which also has the best MP economy in the game), and one Pure healer that has heals that aren't really stronger than anyone's, far less mitigation, and it doesn't even have the MP budget to routinely access those powerful heals without going OOM anyway.
In effect, WHM's heals should all have their MP cost slashed in half and made damage neutral OR SCH/SGE barriers and mitigation oGCDs should have an MP cost on them. And I'm not saying this by way of suggestion (I don't know that it's a good idea at all to do it), I'm saying this by way of "for it to be balanced". Alternatively, WHM should get a second mitigation/half CD on Temperance and a party Barrier effect of some kind, possibly from Plenary. Plenary's 200 potency on every AOE GCD heal for 10 seconds creating barriers that stacked instead (or even that didn't) would be kind of interesting, and basically just an inefficient Panhaima with more steps, and math out to ~800 potency party wide barrier every 60 seconds. But it would at least be something and wouldn't be homogenizing too much since it would still be pretty distinct.
If either one brings something wholly unnecessary, they start to seem redundant, but, perhaps worse, if both are required then you have a very high chance of "Death by composition check," which would ruin any matchmade content unless it badly worsened an already bottlenecking queue by truly splitting it into those sub-roles.
I think that's the reason they made Barrier healers so strong in healing, so that for anything less than Extremes (matchmaking doesn't do Extremes, Savages, or Ultimate unless you specific que, and most people use PF since coordination is needed anyway), it's irrelevant. That's why 24 mans routinely will make the parties something like WHM/AST, SCH/SGE, SGE/SGE instead of taking the WHM or AST from Party A and swapping them with one of the SGEs from Party C. It's just so irrelevant it doesn't matter.
Personally, I feel like the distinction, if it's to be drawn up roughly as it already is now, should simply come down to different particulars of ease. Pure Healers should be better able to salvage stepping in fire when you step in the fire. Barrier healers should be better able to keep you from dying (to unavoidable damage) because of having stepped in the fire almost a minute ago (via vuln stacks) and occasionally sacrifice their own would-be damage for others' uptime.
This is a possibility, but I think it goes to the above. WHM GCD heals are too MP inefficient to make that work, and they're sacrificing a lot of DPS to do them. Making WHM GCD heals damage neutral via Misery and half MP cost would actually make what you say above a reality.
WHM should either have the most efficient heals in the game OR the largest (or both). It really doesn't. All its non-Lily GCD heals are comparable at best to the other healers while costing as much or more MP. You can point to Lilies, but Lilies aren't up all the time and are just MP free versions of Cure 2 and Medica, which other healers match with their oGCD suite. A 600 potency Durchole (or Lustrate) can be weaved after a Dosis (or Broil), both of which also have an average of 1 generated per 20 seconds (and SGE can bet +1 every 90 seconds or +2 per 3 mins with Rhizo and SCH able to get +3 per 3 mins with Dissipation), both SCH and SGE's generating MP, and SGE also gets 170 heal potency more from their Kardia, making their version better than a Tetra weave and ALMOST as good as a Cure 2 (DPS loss) or Solace GCD. And there's a similar argument with them having an answer for Rapture with Indom + Sacred Soil (also 3 uses per min, +3 every 3 mins) or Ixo + Kerachole (also 3 uses per min, +2 every 3 mins via +1 every 90 secs). So even its "efficient" heals that refund the GCD are exceeded by the two Barrier healers healing. And not, this is raw potency only, I'm not counting Sacred and Kera's 10% damage reduction here, which makes things even more lopsided.
WHM's heals are not bigger, and not more sustainable, and outside of Lilies, cost it damage to use, while also not offering the superior advantages of mitigation. The ONLY exception is Cure 3 if you need to spam it, but that is ONLY raw healing and not sustainable between the MP cost and loss of old Thin Air, and is a DPS loss to boot.
.