Isn't grayscale really rare in Westeros?
That was my impression, too, but it becomes more prevalent in cold, damp places, like the Iron Islands or Dragonstone. White Harbor is certainly a cold place, and considering it is right by the water, it’s probably quite damp, too. Also, it seems to be more common amongst children, for whatever reason. There would be no lack of pious parents at White Harbor sending their afflicted children to someplace, any place, that might profess to treat the disease.
Also, what about travelers from Essos, where we get the impression from ADWD that greyscale is more widespread? There must be a reason greyscale is rarer in Westeros; the Narrow Sea funnels potential contagious sufferers down to a few ports of entry. Considering the nefarious reputation of the disease, it wouldn’t surprise me if Westerosi were especially alert to it, even if the chance of contracting it as an adult is really quite unlikely.
All of this is purely speculative, I realize.
A septon hospital somewhere would be cool, but yeah I wonder how many cases of greyscale you’d have in Westeros, let alone the North, and if anyone outside the Citadel would bother treating it (weren’t some just sent off to Valyria?)
In medieval times, hospitals were administered by the clergy more often than not. Even if we set aside the whole greyscale element, I think there’s still a lot of potential in the idea of a septon-run hospital. It could also double as lodging for travelers (“hostel” and “hospital”).