Anonymity is not a band-aid, but a fundamental component of privacy. Privacy is an important right which people often take for granted and its erosion makes people less free in a multitude of ways. Even the expectation that one might be surveilled can change a person's behavior in profound ways (Foucault's panopticon has never been more relevant).

It comes down to the fact that other people may do things which we find distasteful or even offensive. You will never, ever be able to get a large group of people to conform to standards of personal behavior to the extent that this is not true, and so privacy becomes a necessity. But as long as those things aren't causing real harm then they simply aren't my business or that of the government.

In my opinion the only worthwhile discussion when it comes to privacy is what constitutes harm and whether a given harm is possible to prevent without causing even greater harm through restriction of privacy and anonymity. In many cases when it comes to safety and privacy, the cure can be worse than the disease.