What’s the point of Physick for Summoner?

[Absimiliard]

From a lore standpoint, Red Mages use a combination of (present-day) conjury and thaumaturgy.

Note that RDM does in fact utilize variants of full blown white and black magick, per the job questline. The forbidden nature of those practices was circumvented the same way RDM's own forbidden nature was circumvented; utilization of one's own aether reserves rather than that of their surroundings.