McCain knows he isn’t returning to DC and can no longer perform his responsibility to the people who elected him, misguided as they were. Why on earth would he not give up his seat? (Rhetorical question. Its because he is a complete ass and hates Trump.)
Because if he does the governor will appoint a successor to the seat and apparantly McCain wants it to be his wife but that's not popular and the Governor is facing his own election. So until he gets a promise that he gets to pick his own successor, he's not giving it up. Or perhaps whoever is pretending to speak for him. Either way, I Think that's what's going on, and he's using this looming SCOTUS battle as ammo to force the governor's hand.