I would agree that healers are kind of poorly situated for FFXIV's demands of consistent damage output while also handling all the mistakes of the party. There's no room for complex DPS rotations, when healers also have to handle additional mechanics (unavoidable heal checks) as well as rezzing/healing/shielding people who mess up. But then when no mistakes are made, or the heal checks are too lenient, there's nothing left to do but DPS. So healers need some kind of DPS tools that don't get in the way of healing when it's needed.

Unfortunately the devs have tried to handle this in the most ham-fisted way possible - removing DPS tools and buffing what remains - instead of just making rotational mistakes less punishing.

They have already done this for other jobs, so it's not hard to imagine. Allow the DoTs to stack up to 60 seconds. Put charges on big damage abilities. Lower the cooldown of 2-min buffs to 115 seconds to counteract drifting. Make all (or most) healing GCDs refund a little damage, similar to Lilies but not a full refund, and ideally using different job mechanics that are interesting in their own right. (Heck, Toxicon already exists, just buff it to be worthwhile.)

These things make it easier to achieve acceptable DPS without removing much gameplay (unless you really enjoy tracking several cooldowns and hitting them exactly on time, sorry). Then they can add more offensive options without over-burdening newbie healers.

The only problem after that is button bloat, but I think there's plenty of options for trimming that down. Combine less valuable/interesting abilities into one, and put combo actions (e.g. Seraph/Consolation, draw/play) on the same button. I don't feel the need to elaborate further, because there's examples all over the forums.