F3 battlecruisers and the cancelled American capital ships

Which practical unbuilt warship designs are especially interesting?

The preferred British example is F3 with 15-inch/50 guns; the cancelled 1920 South Dakotas and Lexington battlecruisers are also considered consequential alternatives.

The F3 design with a 15-inch/50 gun is the preferred British example of an interesting unbuilt ship. A hypothetical choice of F3s in place of Nelson and Rodney is judged better suited to the navy's developing task-force approach. The argument also imagines later ships and refits using that gun, including King George V-class battleships with nine 15-inch/50 weapons. A 15-inch/45 is another possibility for the refits, depending on the choice made at the time. This is explicitly a judgment influenced by hindsight. For the United States, completing the 1920 South Dakota class and Lexington battlecruisers is expected to produce a different fleet for the Second World War. The Dakotas receive particular weight in the assessment, although no detailed American war scenario is developed.