Why the Royal Navy would not keep Takao

What would the Royal Navy have done with Takao as a war prize?

Probably scrap it, because the Navy had no useful role or spare crew for an unfamiliar damaged cruiser late in the war.

Takao would probably have been scrapped instead of commissioned as a prize. The Royal Navy already struggled to crew its ships at that point in the war. Older vessels were rapidly leaving commission so their crews could man new construction. A captured cruiser offered no sufficiently useful role to justify adding it to that burden.