You actually don't need radar, and ATC can do non-radar "procedural" control where they block off sections of airways or entire airports, one-in one-out at a time, like sections of railroad track. There are still a few parts of the remote US, as well as large sections of Northern Canada, where radar coverage is nonexistant and ATC is done via procedural control. Radar outages also happen on occasion, which would necessitate this.

As for lack of radio, this would only work if ATC blocked out your entire route from start to finish - which isn't practically ever done. Otherwise, they need to be able to maintain positive control over your flight since the airspace isn't reserved, which means conflicts are possible.

If you lose radio communication, it's an emergency and they'll move everyone out of your way. This doesn't work very well if everyone loses radio communication simultaneously.