This includes the internet. All such traffic should only be accessible by the ordinary public, through particular 'publishers' and 'providers'.
We have to decide between Anarchistic Democracy or Altruistic Democracy, and Tyranny - very difficult!
Short of shutting down the internet and beginning all over again in making an network that could limit and track messages, once more the battle is over with no matter what laws are pass.
My isp or the government can only read the traffic I do not care if they read or not read and trying to change that given the very foundations of the technology is a losing battle.
China can not do it and even NSA of the US government can not do it.
Nor can all the governments in the world control the public postings on websites and at best all that would happen is that websites would go to the darknet where there is zero abilities to track them down.
To sum up you can not uninvented either the printing press or the internet.