You still need to exchange keys. You can't get around that. Otherwise, how do I know the public key you sent me over the radio is YOUR public key and not someone else with a more powerful radio?

By having the key signed by someone who you trust. Which in a military typically means the central command.

Sure, but then you need the central command's public key in order to verify that signature. How do you get that?

Ultimately it boils down to you needing to bootstrap your web/chain of trust somehow. In a military it might be easier; radios would be distributed to field troops with the needed trusted keys already present.

But more "public" radio? We don't have a sort of "radio CA", and there are no radios that know how to deal with such a thing. I suppose we could reuse the TLS CAs, though, and build SDRs to use it, which wouldn't rely on any particular hardware. But the point is that this just isn't set up at all.

You still need to physically meet someone you trust to exchange keys, however you slice it.