There would also be a requirement for all playback to actually properly check the private keys and for all the parties involved in the process to be acting in good faith. Not only would you have a black market for individuals to scalp clean keys but you'd likely have nation states with interests putting pressure on local manufacturers to give them backdoors.

We'd probably hit a lot of that with SSL if it wasn't so unimportant from a political perspective[1]... but if the thing we were trying to secure is going to boost or damage some prominent politician directly then the level of pressure is going to be on a whole different scale.

1. And we might still have that corruption of SSL when it comes to targeted phishing attacks.