I'm aware of the constraints inherent in designing equipment for this kind of demanding physical environment, but with reprogrammable chips being the norm rather than the exception, I'm really surprised that more modern cryptography isn't expected from these radios.
Military radios absolutely do have modern cryptography. That is half the reason why the NSA exists.
If you think you know better most likely you are wrong, or you are seeing some system which is held back so they can maintain compatibility with coalition forces.
You don’t need revocation certificates to zero out the key material of a radio. In fact it wouldn’t work reliably because it assumes all network participants are within radio range and listening when you want to zero your keys. Much more easy and reliable is to delete the key material localy on the radio. This zeroing can be also performed by a remote signal.
Only if they are unprepared. They can agree in advance a time and a location to meet when things go wrong. Then the only thing they have to broadcast on the radio is that the radios have been compromised and the backup protocol is active.
> there could be a 'dead-man switch' or emergency button on the radio that would send a revocation certificate to all the other soldiers' radios
I’m not sure i follow what you are saying. Are you proposing a button on the radio which removes that specific radio from the network? If so that can be much more easily, and reliably, done by zeroing the keys of that specific radio.