In the time period I study, some navies did experiment with distillation systems (there's a small still aboard HMS Victory), but they were not particularly scalable/useful until the principle of distilling water and compressing the steam was tested, slightly before WWII. At the time of the Ancient Mariner (published in 1798 with the conceit that the mariner would have been, you know, ancient), it was much more efficient for ships to carry water with them and resupply fairly frequently at known sources of water.

Storage was always at a premium aboard ship, and while distilling seems efficient when you're out at sea, the rough rule of thumb is that it takes an equivalent amount of fuel to distill water with your output (that is, a gallon of fresh water will take a gallon of fuel to distill). That rule of thumb relates to a liquid fuel like gasoline; wood, being less thermally efficient, would be less efficient in distilling water at that point.

So it doesn't make a lot of sense to carry distilling equipment when ships were generally near sources of fresh water, and/or could rely on rainfall (most ship captains would collect rainwater when possible, using sails as funnels).