They went with "Trials and Tribble-ations" instead.
Yeah, and that was just a mockery of TOS.
I'm surprised that none of the other Trek incarnations didn't follow up on "The Doomsday Machine." The end of the episode even goes so far as to suggest that there could be another Planet Killer episode with the characters suggesting "Who knows how many other 'doomsday machines' wander the galaxy?" Of course, I'm sure the real reason that the other Trek shows didn't have another Planet Killer is because they realized they were far inferior to TOS, and trying to do an episode with a Planet Killer would have emphasized the difference in quality between their crappy PK episode and the TOS PK episode.
But the other shows aren't canon, anyway. I would have been happy with ANY follow-up to TOS in general, but we never really got any that I and others can consider canon.