That'd be something like players having lower output when on the verge of death (e.g., 1% less output per %HP missing below 50% HP), and/or the ability to cleanse Damage Dealt Down stacks, though that "healing" then would be solely Esuna.
In that gamestate, you'd maybe want to save ST oGCDs just to more quickly pop people's HP back up after unpredictable damage that isn't best solved via just another AoE, while using precast GCD heals on the more predictable stuff. That in turn would probably have us want a bit more granular control over the timing of our heals, etc., none of which would necessarily be bad.
However, it would ultimately be actions done and considerations made to increase rDPS... not survival. Which is not a "need" so much as a "want", as there is very little chance of that being significant enough to really impact one's chance of hitting Enrage (especially compared to just not letting people die, not wasting GCDs, and keeping one's casts rolling, as per now).
A commonly mentioned dependence on using or not using an additional tool, for instance, has been less than 10% of maximum DPS, which in turn tends to be at most 1.5% of party DPS -- i.e., negligible to one's chances to hit enrage compared to any given mistake that'd be easily visible to others or even just standard deviation in/from Crit/DHit luck across the party.
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Unless you specifically nerf of the damage contributed by the existing tools, allowing Healers more damage through their agency does not at all affect the engagement required of others. It's excess to requirement, and therefore will not affect those who do not wish to use it.
If Healers are not indirectly buffed through those new actions, and their PPM is instead siphoned off from their filler action, etc., to support the bonuses-over-filler of the new skills, then that loss possible would still negligible (e.g., under 1.5% of party DPS). However, there seems little need to avoid buffing healer damage, given that healers are already the role most likely to be skipped over in favor of others, so that is pretty well moot.
Requiring more healing, however, will affect all players, whether they want it or not -- because it's healing, and the only way to require healing is to make the party die when the healing is insufficient.