On the one hand, that was some serious reading fail on my part. Apologies for that.
On the other... it's boggling my mind a bit that the Sky Pirate coat could be considered not-job-appropriate to the extent of being singled out as an "immersion breaking" glamour.
As soon as the replica gear was released and I could look at it as something to use for any job I wanted, I immediately thought it would go perfectly with the Lv60 Scholar relic gear, and I've been using it combined with the relic hat and gloves for my Elezen alt. It looks like a scholar outfit to me, and not like I've borrowed tank gear for it.
I wouldn't personally see anything wrong with it being used for the other healers, either. In fact it's exactly the sort of thing I'd be looking for to put together a masculine healer outfit - elegant and fitting, while still having a long coat so it looks great in motion when casting spells.