I would like to preface by saying that no, I don't believe SGE is falling behind other healers or incapable of performing in the same content. I'm well aware that its personal damage is the highest among healers at the moment, and it is not hurting for buffs. I do however believe there is room for improvement, and given that SGE has a bit of a barrier to entry, increasing a potency value here and there can serve to reduce it.
The most obvious detriment of SGE is its lack of any "Oh Shit" tank heal - no Benediction, Essential Dignity, or even Excogitation. This puts SGE at a particular disadvantage when paired with a DRK, since without a full pool of resources and cooldowns we have no response to the activation of Walking Dead, besides simply watching the tank die.
However, I will also acknowledge that the challenges of Living Dead are failings of its own design that all healers are subjected to and DRK most of all, and this isn't a thread about DRK or its sustainability. Under normal circumstances, a SGE's ability to curb spike damage for tanks with its numerous mitigation effects means it should not have a great need for any specific tool to recover from it... at time of writing this.
(Though I wouldn't be shocked to see one provided next expansion, alongside a reduction to Pneuma's CD, a Pankardia effect and an extra charge of Rhizomata.)
The main issues I would bring up instead, are tied to SGE's core healing philosophy and relationship to its barriers.
First I want to bring up Soteria.
In theory, it's SGE's response to SCH's Aetherpact as a means to boost our constant, passive healing output into a focused healing stream while allowing us more uptime. Potency-wise, it's actually slightly stronger than Fey Union already.
But, I would also acknowledge that Kardia and Soteria only have an effect when the SGE is using its uptime to attack, while Aetherpact can also be used to double-down on focus healing. If you stop to put up a barrier or focus cast a heal, Soteria's effect is going to waste.
(This is also to say nothing of Soteria's effect window being affected by ping, and Aetherpact's advantages of being able to be stored, toggled at will, and extended by certain attacks even during its window.)
Which also puts SGE in an unusual spot of bother concerning its Addersting mechanic. Since Addersting can only be actively generated and consumes an entire GCD to generate each time, the fact that Toxikon is both A) the exact same potency on a single-target as Dosis and B) 5p weaker per-target than Dyskrasia on multiple targets, actually comes out to it being a slight damage loss - not even recouping partial damage lost to casting the barrier unlike Afflatus Misery - with its primary advantages being its instant cast time over Dosis and increased range over Dyskrasia. Given that we can already slide-cast and weave after each attack anyway, this is a relatively rare utilitarian benefit.
Lastly, I'd like to address Pepsis, SGE's response to SCH's Emergency Tactics.
While it's exceptionally good for group-healing when it consumes Eukrasian Prognosis, it's underwhelming when consuming the single-target Eukrasian Diagnosis.
On the one hand, it does not matter how much of the barrier it consumes; if there's only a tiny sliver of barrier left at the moment you activate it, it will give the full potency of the heal. It can also critical heal separately from the original cast.
On the other hand, it comes at the cost of Addersting, it has no effect on Differential Diagnosis, it's usable only half as often as Emergency Tactics, and its healing value doesn't increase at level 85 when the values of our barriers do. Even if it does get a critical effect, because it doesn't consume Differential, it will only give half the healing value of ET. Given the number of times I've gotten an Addersting off the first auto-attack of a boss fight, the luck and timing you would need to successfully get the value of "consuming a partial barrier for a full heal" is exacting.
So my instinctual thought is to ask to "increase Soteria's effect to 100% healing during its window (possibly on a stack system), increase Toxikon's base damage by 20-25% or reduce its falloff, and have Pepsis consume Differential for a bonus heal and return an Addersting if it consumes at least one Eukrasian Diagnosis," but I'm willing to defer to members of the community with more experience for their thoughts on SGE.