Wikipedia's plot summary says (emphasis mine):
Earth has established a totally balanced and ecologically stable underground society (similar to that portrayed in Asimov's novel The Caves of Steel). But one man, Cranwitz, regarded as a deviant and eccentric because he keeps a few animals as pets, refuses to get rid of these animals, the last non-human inhabitants of the planet.
He is finally persuaded by his sector representatives to exterminate his pets, but also commits suicide. This leaves Earth in 'perfection', with its fifteen trillion inhabitants, twenty billion tons of human brain and the 'exquisite nothingness of uniformity'.
I found it via this Reddit post from someone seeking the same story, which showed up as one of my Google search results (buried under a lot of links to Sara Zaske's short story "The Last Zoo") when I searched for
short story "last zoo".