Why County-class cruiser conversions made little sense

Could British County-class cruisers have received conversions like American Baltimore and Oregon City cruisers?

Their old, heavily used hulls made the conversion cost unjustifiable when Britain was already reconsidering the cruiser role.

The County-class cruisers were 1920s hulls heavily worn by service in the Second World War. An expensive missile conversion of those ships offered poor value. Britain was also reconsidering whether it could afford traditional cruisers in a substantial role. Its later County-class destroyers performed cruiser work under a different label, while the Tigers provided a minimal 6-inch gun cruiser.