I think there would be an ever better angle to this. If the government can listen to any legally encrypted communication via their backdoors, then by definition any communication they can't listen to is illegal and they can focus their intelligence resources people communicating in such way.

But honestly, I think it'll result in bad guys using the same backdoored crypto that everyone else will be using, relying on steganography and disappearing in the noise - so basically, they'll do things in the same way as they always did, since assuming all communications is broken by the government is simply good OPSEC.