Why the US Navy stayed with the five-inch gun

Would a 5.4-inch/48 gun have served late-war and postwar US Navy ships better than the long-barreled five-inch gun?

Not by enough to justify abandoning the five-inch system and the industry and infrastructure already supporting it.

The proposed caliber was roughly 130 millimeters and could offer some ballistic advantages. Those gains were too small to make the established five-inch weapon a bad choice. American factories, ammunition supply, maintenance practice, and training already supported the existing caliber. A merely better specification can lose to a weapon embedded in a complete industrial system.