F3 battleships and a standardized 15-inch fleet

Would Nelsons built with 15-inch guns and more speed have been better for strategy and logistics?

Yes; the F3 route offers faster ships, common ammunition, and a stronger incentive to modernize the 15-inch gun family.

Building faster F3-derived ships instead of the Nelson class would preserve a common 15-inch ammunition and support system across much of the battle fleet. That continuity would make a later return to 14-inch guns for the King George V class harder to justify. More importantly, a new interwar 15-inch weapon could use improved metallurgy and a longer barrel rather than relying indefinitely on the First World War design. New turrets and guns might then be adapted to older 15-inch ships during modernization. The gain is therefore strategic mobility and fleet-wide logistical development, not merely a different silhouette.