Why a 60-caliber 5.1-inch gun brings diminishing returns

Would a British 5.1-inch/50 gun have been replaced by a 60-caliber version?

Probably not; the extra length would impose barrel-life, weight, and high-angle-fire penalties without enough operational benefit.

Moving from a 50- to a 60-caliber barrel would reduce barrel life and make gravity-induced droop more significant, especially under frequent high-angle fire. The comparison with later American 5-inch/62 weapons is limited because those guns benefited from decades of improved metallurgy and had different tactical demands. Later weapons also relied less heavily on sustained anti-aircraft fire from the gun itself. A mature 50-caliber weapon would already sit near the practical upper end for the proposed wartime role.