Why 125 mm did not become a wartime destroyer standard

Why did no major navy adopt a 125 mm destroyer gun during the Second World War?

Because established guns around five inches already filled the role, and a new 125 mm caliber offered too little benefit to justify separate production and logistics.

A 125 mm weapon offered too little distinction from existing destroyer calibers to justify another ammunition and support chain. Navies already had mature guns around 4.5, 4.7, 5, and 5.1 inches, each embedded in national production and doctrine. A navy using 120 or 127 mm weapons gained little by inserting a caliber between them. Logistical standardization and existing factories can outweigh small theoretical differences in shell size.