If we want to make the relationship between pure healer and barrier healer more distinct and meaningful, a hurdle you have to deal with is ensuring both feel good during 4-man content, especially if Criterion is going to be a thing.

The idea of having pure healers have the ability to burst heal while barrier healers can't, and barrier healers have the ability to mitigate but pure healers can't, and the two are meant to cover one another could work in theory. Having this relationship where pure healers are also meant to handle healing checks while barrier healers set up resources before damage could also work. But what you'd need to do for dungeons and easier content is create scenarios where both burst healing and mitigation purposes are needed, or at least make certain mechanics much smoother. Then, you'd need to give pure healers access to clutch mitigation tools that come at some type of opportunity cost, and vice versa for barrier healers and burst healing. This ensures both camps have the tools they need to cover those mechanics when healing solo, but are meant to avoid those clutch actions when together while the other healer covers that gap in their performance.

When I say opportunity cost, it should be a cost of DPS uptime. In other words, in order for SCH or SGE to burst heal, they have no choice but to stop attacking, and spend the next couple GCDs using their clutch burst button. The same is true inversely with pure healers and mitigation/barrier tools.