Q&A: why choose 16-inch guns despite logistics?

Why did the Royal Navy choose 16-inch guns for Nelson and Rodney instead of keeping 15-inch ammunition commonality?

Because 16 inches was the treaty maximum, and the Royal Navy would not accept a visibly smaller main armament while rivals built to that limit.

Keeping 15-inch guns would have simplified ammunition supply across much of the Royal Navy's capital-ship fleet. The Washington Treaty nevertheless permitted guns up to 16 inches. The service was unwilling to appear second-rate by choosing less than the allowed maximum while competitors also built to the limit. The same competitive logic appeared in treaty cruiser and destroyer design. Prestige and relative capability can outweigh standardization even inside a restrictive arms-control system.