The Problem with Healer Feedback, and requested changes

[Archwizard]

Speaking on this SGE concept since it's the healer I care the most about, this solution resolves approximately 0 of SGE's issues. SGE does not have a difficult time healing. It doesn't need to a ton of additional healing buffs, it needs to have gameplay.

And I get that, but the thing I was focused on was changing the use-cases of its spells to improve its gameplay, rather than just "buff SGE's healing for buffs' sake".
It just happens that "changing the use-cases" usually means adding incentives to certain interactions or particular situations. Considering SGE's central conceit is augmenting their own spellcasts, this kind of synergy is... actually fitting for the job.
You don't need to change the use-cases of its attacks generally (particularly since it presently has the most diverse rotation compared to other healers, not to say that it can't be expanded), except maybe Toxikon as you've latched onto.

Diagnosis, Prognosis and Physick are widely considered to be absolutely useless wastes of buttons. For SGE though, the fact that they're changed with Eukrasia means they're here to stay, not something you can just upgrade from Physick to Adloquium. Ostensibly they exist for when the barrier is already active and you need a more efficient form of healing; I just suggested literalizing that, which also gives you something to use when you're doubled-up on barrier healers.

The Eukrasian Diagnosis thing? QoL. When I'm playing SGE or SCH, I always try to get a crit barrier onto the tank pre-pull. Sometimes that doesn't happen because RNG isn't in my favor so I'll cast it 5 times to no avail, but it's also the majority of the time I spend actually casting E. Diag (and the majority of MP wasted in wall-to-walls).
As for the proc, presently SCH has Recitation to force a crit barrier. We don't have anything like that, so the ability to stock up a crit heal in advance would balance that out without having to hard copy it.

Soterion has extremely limited uptime, and if you actually end up casting anything besides an attack that procs Kardion, you could end up losing the effect before using them all. This means you can actually use those stacks, and it also gives you a benefit of mixing in a Synastry-like effect in the odd case you need to panic heal (which is actually SGE's major weakness as a healer), or duo heal (thereby capitalizing on Kardion's ability to let you multitask).
Plus, Soterion amounts to barely more than a Diagnosis... over 10 seconds. Barely more than our other HoTs either, which are AoEs. I don't think anybody will argue if you were to say Soterion needs a buff.

Phlegma... is a personal indulgence. It's partly because I've seen threads about being trying to match every healer's AoEs up to Holy, which I personally disagree with because that just invites homogeny and most forms of CC aren't equal anyway, so I think each one could use some unique flavor for AoE phases (like the Spikes effect I suggested for SCH).
Not to mention that Kardion is presently an extremely underutilized healing tool in terms of SGE's design (every attack has its own potency to proc it... but the potency is always the same?), particularly since healing requirements are higher during W2W. If the devs won't turn every Dyskrasia into a Nascent Flash pop (which, fair), we might be able to meet in the middle with a more limited ability like Phlegma.

Sorry you hate the place Toxikon is in right now, but this is an attempt to resolve it as it is. The devs wanted to experiment with a new means of getting an instant damage tool besides literally copying Ruin II or Aero, and considering how many instant non- or light-damage tools are already at SGE's disposal I can't blame them for coming up with this.
While I like the idea of "use barrier to generate a counterattack," it isn't realistic for most content. There's no way to design it to be useful just for counterattacking tankbusters without accounting for the fact that nearly every autoattack in Savage basically is one. If Toxikon is a damage boost to fish for then you end up with a system where SGE is just spamming barriers on the tank until its MP runs out.
So yes, I agree with the suggestion of Rhizomata as a means to generate Toxikon because we actually do need a means to generate more charges without incurring a damage loss. I don't think it "destroys Rhizomata as a healing resource", dunno where you get that from, especially with Toxikon presently being damage neutral.