How Italian rebuilds widened the capital-ship race

Were the Italian battleship modernizations worthwhile, and how did they affect the capital-ship race?

Yes; the Italian response to the Dunkerques helped turn a Mediterranean competition into a wider modernization race involving Britain, the United States, and Japan.

The Italian modernizations mattered because they transformed a French-Italian reaction into a wider race. France's Dunkerques prompted Italy to rebuild its battleships, after which Britain and the United States entered the modernization cycle while Japan already had work underway. Regional competitive moves can reshape several navies' capital-ship programs.