I've always thought the basic single target heals (Cure, Benefic, Physick, etc) should be instant cast. That way you can chase a racing tank with a quick heal that doesn't leave you locked in place. The Free Cure Trait should remove the MP cost from Cure instead of making Cure 2 free. This would make spamming Cure a literal way to save MP and offer the exact same advantage of the original Free Cure Trait (but better) since the MP you save could be used on Cure 2. If you die as healer coming back with no MP is like a second death as you're practically useless. Making Cure free would offer an obvious choice to get back into the action while you wait for your MP to Regen back to a manageable level. Healers have always been one of the least mobile classes in the game so this change would breathe a lot of life back into the hollow design of CNJ. Imagine being able to run from enemies while you heal yourself with Cure instead of standing there getting slapped in the face as a fresh CNJ.
As for Medica, Medica 2, and Cure 3 I think Medica 2 specifically needs a 30 second duration that can be extended to 60 if cast twice in succession and no hp regen. I would instead let Medica 2 place an effect called 'Faith' on all party members that increases DPS by 1% or maybe Determination by 5% to be more healing oriented but is essentially a buff you want to always keep up that alters WHM spells. Casting Cure on a person with Faith would cause 18 seconds of Regen. Regen as an instant spell would no longer exist. Cure 2 would have its potency increased by 30% on anyone with 'Faith'. Medica would cause an AOE Regen to anyone in range if they have 'Faith' becoming what Medica 2 is now. Cure 3 would still be a massive heal with a small range but increase the duration of any WHM skills by 15 seconds on party members if they have 'faith'. This would give all the GCD spells a definitive purpose.
-Medica 2 is for increasing party DPS by granting 'faith'
-Medica is your standard AOE heal that causes a party Regen with 'faith' active
-Cure 3 is your powerful AOE heal that extends WHM effects by 15 seconds with 'faith' active
-Cure 2 is a powerful single target heal worth slightly more than Tetragrammaton and Afflatus Solace with 'Faith' active
-Cure is always available as a free instant cast GCD heal that causes 18 seconds of Regen with 'Faith" active.
This gives the core GCDs a reason to exists and even prunes one spell in the form of Regen which could be repurposed as an attack if we're lucky and hopefully not something boring like Glare IV every two minutes.