A Soviet missile battleship could prompt a joint NATO design

Would Soviet missile battleships lead NATO countries to pool resources for their own missile capital ships?

Probably not through pooled construction, but NATO could adopt a jointly developed class and standardized weapons led largely by Anglo-American technology.

NATO members would probably stop short of pooling ship construction, but common design and development work could produce a joint class concept. Anglo-American technology would set the likely baseline, while individual countries could still build their own hulls. Gun caliber would become an arms-race signal as well as a design choice. If the Soviet ship exceeded 16 inches, the Western response would probably seek an even larger weapon rather than accept a visibly smaller main battery.