I'd be happy [1] with locked-down radio firmware if it could talk only to the radio.
One big problem is that coprocessors in embedded systems often have full access to the memory bus, meaning there's no way to stop a trojan in the closed and locked radio firmware from reading and modifying any bit of system memory, which can include your personal data and encryption keys.
[1] Although I'd hope that it'd still be possible to buy or build a general-purpose SDR.