Technically, you do not need radios. There are many many uncontrolled airports in the United States, where you can technically fly around without establishing two-way radio communication. It’s doable, but I don’t know if that’s even a scenario pilots test in the simulator during their semiannual trainings.
Most air traffic is IFR. You definitely need radio for IFR traffic in for deconfliction in most of the world. (There's a few exceptions in very remote places, but that's mostly academic.) Even legacy procedural (non-radar) separation assumes you have working radio, and a radio failure is an emergency.
VFR traffic doesn't necessarily need radio, and is not affected by this groundstop.
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