The American case depends on Republicans and Democrats supporting the same ceiling for different reasons. Roosevelt gains a long-term cost forecast that can help him secure more ships, while Tillman gains a known upper bound on the capital-ship bill. Britain can exploit its industrial advantage by repeating a mature design instead of moving to a new generation whenever a foreign navy does. The Royal Navy would probably continue building cruisers and battlecruisers, raising the question of how close those categories could grow to the capital-ship limit when lower types had no separate ceiling. British designers would still have to weigh the shell weight and penetration of a 14-inch gun against the lighter 13.5-inch system, so the agreement stabilizes the envelope without eliminating design choices.
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Roosevelt, Tillman, and Britain could support the cap for different reasons
Predictable unit costs could unite American political rivals and let Britain repeat a mature design without surrendering fleet numbers.