The Old Mixer wrote:
I was under the impression that the radioactive bombardment was meant to destroy life, not the station.
Radiation will kill people, not destroy buildings and equipment. So the automated station would still be operational.
Yes, that's why Kirk specifically wanted the planet subjected to a lethal concentration of neutron radiation in the event he failed to kill Mitchell. The neutron bomb
, a weapon designed to cause maximum casualties from radiation rather than heat and blast, was very much in the news at the time.