I would bet the problem is not strictly the radios themselves, they will still work, Planes can talk to each other and directly to airports, But that there is a large scale highly integrated control center network that failed, and planes can no longer talk to centralized traffic control.

So it falls back to local control, more in the style of visual flight rules. Pilots in existing flights will have to be vigilant and do their own deconflictation and stop new flights out until the network is back up.

All conjecture at this stage of course, but all the radios won't just fail. It is probably going to be a poster child example about the dangers of large scale integration. The attraction of course is that integration is very efficient, the danger is it tend to fail all at once instead of in smaller pieces.