About The Green Summoner AKA Scholar

[Rein_eon_Osborne]

First of all. Mana management.

SCH's MP economy is fine as it is. AF and dumping unneeded aetherflow stacks into Energy Drain is all you need besides the maintenance provided by Lucid Dreaming. If you're talking about running out of MP from AoE spamming in dungeon pulls, it's probably because mobs are dying too slowly. If this happens even AST and WHM can still run out of MP. This isn't just SCH's problem. This is your group's DPS member's problem. They could be freestyling, or single targeting in middle of large pulls.

Faeries.[...]
Dont die then, first rule. Fine
But why this job punishes the mistakes so badly?

• WHM = Loses built up Lilies (equates 1000 MP heals each & Misery); Thin Air has a rather long cooldown which makes recovery harder if they happened to go cooldown fairly soon before you die. WHM has the priciest MP cost from their healing spells and quite limited amount of abilities that also have longer cooldowns. If even LD are on cooldown then you're a sitting duck.
• AST = Loses built up seals (your party is missing a valuable raidwide buff, suffers an overall lowered dps). If LD is on cooldown then your Draw 30s should be coming back fairly soon. Besides, AST has plethora of powerful healing abilities with decently short cooldown period.
• SCH = Loses AF stack, fae gauge, & fairy. MP however is still not the glaring issue here. Between Lucid Dreaming, Aetherflow, and dumping Energy Drains, it's fairly easy to gain back large amount of MP from dying. The only gripe here is to summon back your fairy. A lot of SCH's healing comes from their free of MP cost-heals and it's on ridiculously short cooldowns. So I'm unsure what do you mean by "everything you can use needs your MP" when that's more like a dying WHM's issue.

Toolkit.

SCH contributes their heals in a rather subtler way than the other two healers, but they still heal a disgusting amount.
About shielding however: if you haven't noticed already, SE categorizes SCH as a "Barrier Healer" which literally translate into having an "on-demand shielding spell" (Adloquium & Succor) rather than "effective shielding abilities" (Nocturnal Celestial Opposition, Diurnal Celestial Intercession, Divine Benison, Seraph). As you learn to be better however, you will notice players are trying to avoid using their "on-demand spells" because why would they, when they can keep damaging & weave an effective abilities to do the same job, a.k.a. keeping party alive & healthy? Healers are there to keep the party alive, not topping everybody to 100% all the time.