The only thing that would be reduced is that Cure 1 and Medica 1 would be less used in favor of Adlo and Succor...but this is ALREADY the way things are.
You know full well that's not the case in any serious content. The effect isn't just that you use the blatantly superior options that exist now, but you'd use almost only ever the blatantly better-still option that you'd have just recreated, because healers operate
as a pair.
If one healer can freely spam ST healing but not AoE healing and the other has can freely spam neither, then the one with the relative advantage in ST will take up that much more ST duty and pass along that much more AoE healing to be done to the other. The only exception to this is where both healers somehow need to AoE GCD heal within the very same single GCD of time after impact for the raid to survive (i.e., basically never, even with increased healing requirements), instead of being capable of the more efficient combined action wherein the healer less penalized, relatively speaking, for AoE GCD healing does all the necessary AoE GCD healing.
If you make Eukrasian Diagnosis free and nothing else, you'll see more use of EuDiag and less (if any) of anything else.
Inb4 "But you defended people using GCDs when necessary even when it's a loss, so why wouldn't people still use the other GCD options!" Why? Because the others wouldn't be necessary outside of the aforementioned incredibly rare situations. You will thereby have reduced the number of competitive choices by overpowering the single choice among many.