There's probably some point at which the ways I use that data can be classified as stalking or harassment, but simply collecting it is allowed.
What about the embarrassing things other people post about John Doe? What if this harms his ability to provide for his family?
What about things fabricated by others to silence or overtake John Doe?
edit: (adding the point below)
Just because it's legal to collect, manipulate, and profit from this mass of information 'somewhere' doesn't mean that concerned groups of people shouldn't try to make that process harder or impossible.
Is "John Doe" a politician trying to suppress public discourse about a scandal?
If you do something embarrassing, and people are talking about it, it is absolutely immoral to use government force to prevent people from disseminating information about it.
> What if this harms his ability to provide for his family?
Of course, think of the children. We must suppress any information that could negatively affect a hypothetical child!