What unbuilt age-of-sail warships are most interesting?
Short answerThe most interesting examples are the very large ships of the line planned near the end of the Napoleonic Wars, whose completion was overtaken by peace.
NotesThe later ships of the line whose development was overtaken by peace are the main interest here. British plans for very large sailing warships stand out as the most intriguing unbuilt category. Because the Napoleonic Wars ended before those ideas were completed, their performance remains hypothetical. The answer raises a design-history question: how far late-sailing-warship development might have gone if strategic and financial demand had continued.