I agree with a healer redesign from a kit perspective, but they do have to be careful about how much they nerf the healer / tank kits. If they nerf it too hard then then we will run into necessitating gear before being able to clear content that would lead to 3-4 week clears that we saw in Gordias and Midas. I know not everyone will think that's bad but at the same time there those two raid cycles nearly buried the raiding scene six feet under as well.
I also feel the difficulty of the healer checks revolve around how mechanics are made too for Savage tier content. A failed mechanic is either a wipe / death, so there's nothing to "heal" per say. We either heal that raid buster or pick that person up off the ground with few things in between usually. More Prey type mechanics and more frequent tank buster mechanics (even shared to put emphasis on the myriad of mitigation tools available to a raid) would help out with that. Reverting MP tools to how they were in 3.X would also increase the challenge of resource management.
I wouldn't mind a higher healing check - I am generally an easy person to please in terms of content so if they kept content as it is or start tweaking to frequency of unavoidable damage, I'd find a way to work around it and enjoy myself. I'm one of those types of players who believe that a healer's primary function is maintaining party health but at the same time I understand that's an extremely low bar too if all a healer does is push green-healy buttons because that's how it feels healer's were design - huge heals at the press of a singular button. I've always felt healer's were designed to be "easy" in XIV as a means to encourage more casual players to try it out but that then leads to high-tier healers being bored out of their mind if they aren't using their DPS abilities.
Hopefully we see a change in content and healer design in 5.X to actually make raid healing more challenging from a "healer" perspective.