Did the US Navy have an institutional preference for main-gun calibers in whole numbers?
Short answerYes; it preferred larger two-inch steps, which also helped present each caliber as a clear advance to Congress.
NotesThe US Navy preferred two-inch jumps, often positioning them as an answer to British increases of an inch and a half. Moving from 14 to 16 inches also made the next British step awkward unless Britain jumped all the way to 18 inches. The pattern mixed institutional habit with competitive signaling to Congress and foreign navies. Caliber choice thus carried political meaning beyond ballistic performance.