With this thread I'm thinking from your average user perspective rather than my tech savvy one.
We both know that at any time a web owner could go in and access whatever they want, which isn't a bad thing. But what people do in private in my opinion is up to them and does not warrant a third party to intervene between their business and the other person unless something is reported.
I will give you this positive point, it would make illegal activity that is being conducted in private to be more easily tracked and appropriate action to be taken. So for that reason alone I'm no longer opposed to this idea.
But I can't promise my support for it either.