Aight so, two notes:
To the thread title, I think RDM's high potential with Verraise as-is kinda supersedes the inconvenience of it being so late in level? Like, the impact of healers or even SMN having raises (which they still must either swiftcast or hardcast) is EXTREMELY different from the impact of RDM's ability to rez spam. It would make sense for RDM to have it at such a low level if the job had, say, a limiter on how often it could Verraise to keep it in line with SMN and healers, but that's just gonna lead to hard-nerfing the ability unnecessarily. (After all, most high-end content is balanced around the assumption you'll be avoiding raising where at all possible, so the boon it provides is mostly in easing casual play.)
Plus, classically, Red Mage gains White Magic spells at later levels than dedicated White Magic users. It would probably be the same for SMN if not for being conjoined to SCH.
And I think it provides a sense of advancement once you get significant spells like Verraise while leveling (especially when most of your alternatives are passive damage traits), which you might overlook if you already had it as soon as you picked up the job.
To the discussion of AoE healing: I don't think RDM should get some kind of Medica. Practically speaking, RDM doesn't need the extra button wasted on a healing spell, especially since the job itself is not focused on healing and the continued existence of Vercure in our arsenal is justified by its impact on our DPS (by means of giving dualcast during downtime or untargetable periods).
BUT! I can see our existing Vercure getting an upgrade to provide splash-party healing around the target (probably in an exceedingly small radius akin to the original Cure 3) as a means to boost raid utility during downtime without increasing button count -- "I can assist in topping everyone off in limited circumstances, and am in fact encouraged to, provided that it doesn't interfere with my damage-dealing." You still don't need to target anyone with it since it will auto-splash off you, but still have the convenience of being able to heal faraway targets in a pinch. (As long as I can still target it on other players I'm not partied with like with current Vercure or PvP Cure 3, rather than it being party-only like PvE Cure 3.)
I feel like RDM should, at SOME point, get either that or a Warden's Paean/Erase type oGCD as a "Veresuna", but not both. It's a DPS with some healing utility, yes, and arguably should have more healing utility than most DPS... but it should still be relatively limited compared to an actual healer.