A pilot WILL land, even without clearance. They're not going to crash their own plane. Either way, ATC has fallback procedures and can just use radio to communicate and manage everything manually. Get all the planes on the ground in safe order and then wait for a fix before clearing new takeoffs. https://aviation.stackexchange.com/questions/43379/is-there-...
Planes always get landing clearance via radio. "Planes in the air were unable to get clearance to land or divert" strongly suggests that the radios themselves were not working if it's actually true.
