I would argue that you would still need privacy, in so far as to allow an amount of time in which you could form your dissenting thoughts in private, write them down, iterate them before you go to the street corner and announce them to the world.
If everything was in the public space or monitored then people with dissenting ideas may not have the will or motivation to iterate on them as is necessary to create a well reasoned thesis, and hence they would fall flat or be cast out as just another nut job.
Oh, no - I'm not trying to downplay the need for privacy. I'm saying that privacy and anonymity are two separate things and people too often mistake one for the other. Privacy is everyone's right, but it has nothing to do with dissent. Blasting your opinions out into public while shielding yourself with a pseudonym isn't privacy.
I consider that anonymity and pseudonymity are aspects of privacy. What's private there are the associations between activity and identity. We need "privacy for the weak and transparency for the powerful" (see Cypherpunks: Freedom and the Future of the Internet by Julian Assange et alia).
If everything was in the public space or monitored then people with dissenting ideas may not have the will or motivation to iterate on them as is necessary to create a well reasoned thesis, and hence they would fall flat or be cast out as just another nut job.