It wouldn't. But convincing people may be easy. Just wait for the next bomb to go off or something, then say they were using encryption in their communication.
For example, by logging all of your keystrokes / input actions and storing them. (edit: this is why people are so concerned about things like Intel ME)
Well, sending them over the network in real time is one option, or if we are talking custom hardware as in this discussion, then it could be made with local storage (and wouldn't need to be all that big...).
Sending them over the network would be trivial to detect and block, since you could just look at the outgoing packets on the switch the computer is connected to.
That can be blocked. Not to imply that your concern is invalid, but it would be difficult to enforce something like this when a countermeasure can easily be created.
