So in the Age of Sail, a lot of concern was put into making sure the water rations lasted, and being becalmed could be a disaster because there was no way to get more water unless it rained. However distilleries/stills had been around for centuries at this time, mostly for the manufacture of spirits, but did it just not occur to anyone that it could also be used to make seawater drinkable? I mean it probably couldn’t have kept up with the rate at which water was consumed on a ship and the best way to restock would still be rain, but it could’ve at least helped stretch supplies a bit at least. Did it just not occur to anyone?
Some sailing vessels did experiment with carrying small portable water stills. Cook's HMS Resolution carried a small distillation apparatus, although it was certainly not common issue, and there's still a small distillation apparatus aboard HMS Victory. The issue isn't that evaporators were unavailable, but that they did not scale -- you'd have to burn a ship's load worth of firewood to produce a comparatively small amount of water, and ships generally built time for re-watering into their plans. Wooden casks were ubiquitous, but by the end of the period I study, some ships were beginning to use iron storage tanks for water.
In any case, most fresh water aboard ships wasn't used for drinking, but for steeping and cooking salt meat -- estimates are about 90 percent or more.