Per another of OP's comments in this thread, they seem to suggest that CBS (of all organizations) is actually trying to help a Democrat with better chances in the general to defeat a Republican. So, therefore, they artificially manufactured a Streisand Effect stunt by killing the interview.

Because that's somehow a more parsimonious explanation than the clear pattern of Brendan Carr's statements and actions using the FCC to accomplish the political goals of the administration.