How a Tillman battleship could reshape the arms race

How would other navies react if the US Navy actually ordered a Tillman battleship?

Britain would probably answer with a larger or more powerful design because it could not surrender technological leadership, even while continuing its numerical competition with Germany.

The era contained both a technology race and a building race. American, Japanese, and Italian advances could force Britain toward larger guns or ships. German construction required enough British hulls for the North Sea, ships in refit, and worldwide commitments. The Royal Navy could therefore react to different rivals in different ways at the same time.