My take on the simplicity of healers and the healer problem

[Jamini]

That seems like a problem if SCH does 4% more DPS and also has more ultilty, mitigation,and benefit to the team than a WHM. WHM really only has high output GCD healing and spamming glare. It's utility is both extremely lacking to AST and SCH, and it does lower damage.
That doesn't seem quite right from a balance perspective. Not even to mention we just had a tier where AST was absolutely dominant because one of it's buttons was so good it just invalidated a mechanic and it was a must pick, directly bumping out one healer in particular.
Having better damage, better utility buttons, and more options for OGCD healing and mitigation.

AST could also solo heal DSR on patch 6.1 due to it's high damage contribution, high heals, and shield and mitigation buttons.

I do not believe you actually understand what I mean. Allow me to explain it tn clearer terms.

1. You are literally talking about the top 0.01% of all players in the game. SCH and AST only begin to pull away from SGE and WHM when you get to the top 15% of all players who even bother to have cleared savage fights. Right off the bat that's a very small number (something like 10% of any game's population even raids, and fewer will clear even one fight in a tier. Much less all of them.)
2. That 4% is not personal damage. It is raid contribution. So you can immediately throw out all of that utility from additional considerations. Same with Chain Stratagem. Both of those are baked into the rdps number
3. You are correct. WHM mostly has high healing output... and in some fights that is extremely helpful. To the point that in the top 20 parses that are currently on P6S (selected because it's a dummy fight that doesn't really have massively hard-hitting mechanics. IDEAL for SCH and AST) nine of those clears have a white mage! Tied with AST for nine top20 clears! Meanwhile SGE and SCH have 11. The breakdown of healers in the top 50 even skews a little the other direction with SGE and WHM having 29% and 27% of the top 50 overall clears respectively (this week) , and SCH and AST are 22% each (this week)

My point here is that your information is not backed by empirical evidence. If anything buffing healers are less represented at the top, even if they have slightly more contribution. Because ultimately all healers are actually in a pretty good place!

Far as I am aware, exactly one team is recorded doing solo DSR AST. It is one of the absolute best teams in the world.
The damage I am including Is not personal damage either. It's raid contribution (so it includes a portion of all buffed damage, taken from the person buffed.)

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Edit:

I also forgot that you are neglecting to note that WHM doesn't exclusively have heals.

1. Regens. Regens are vastly useful and efficient heals. While technically healing, their fire and forget nature often makes them really ideal for the current structure of high-end fights. (Where you have periods of a LOT of damage, then a long recovery period.) - Pairing SGE/SCH with a WHM/AST dramatically makes the job of both jobs much easier as their abilities are complimentary. (And yes, SCH and SGE both have regens. But WHM and AST regens are notably better)
2. Asylum. While not a mit, the +healing on this works on basically all forms of recovery. It's also strictly better than Fae Illumination (which only impacts spells) and combos really well with tank heals like Shake it Off, Aurora, Heart of Corundum.
3. Divine Benson. While ST, it is a shield.
4. Temperance. AoE mit and healing up. Core for WHM play in savage content
5. Aquaveil. A single target mit. Comparable to both skills on SGE and AST.
6. Liturgy of the Bell. A beautiful combination of Panaheima AND earthly star. While it's not a shield, this ability basically means I as a Scholar do not need to do much of anything except pop soil during the entire duration. It's insanely good.

Could WHM do with a group shield? Yes. Do they starkly need it? Not really. Again the difference between the best WHM and the best SCH or AST is a minuscule amount, even less when you consider that healers are less than half as much damage contribution as a DPS is.