Why not adopt the US Navy 5-inch/38?

Why not convert the Royal Navy to the American 5-inch/38 instead?

Converting the fleet during wartime would impose an enormous logistical and industrial burden, while British industry was capable of developing a suitable domestic weapon from its existing 4.7-inch base.

The US 5-inch/38 provides a useful performance comparison, but adopting it is not a simple purchasing decision. The Royal Navy would have to change production, mountings, ammunition supply, training, and support across a large wartime fleet. The alternative redirects British development effort toward a weapon and industrial base already in service. British programmes had chased an ideal new solution instead of improving the available one soon enough.