Degree of anonymity is subjective. Very few people want full secrecy (ie off-grid), because to have a functioning society, there has to be government (read: civil protection) at some level. It can be Federal, State, County, Parish or Local, but human society is made of connected individuals.
All those levels of govt. are interested (and not interested) in various degrees according to their remits.
The privacy is not for gov, its for the people, gov should be as transparent as possible and people's stuff as private as possible, this is the ideal society.
I myself, do not want full secrecy in the sense that no one, even myself, can see my transaction history when it comes to transmitting money. Have you not seen the bombings that threaten cities worldwide? From the boston bombing that claimed a few lives, to ISIS taking over bases in the middle east?
Full secrecy would allow child molesters, terrorist organizations, violent racial groups, gangs, corrupt governments(north korea), etc to grow even more without anyone being able to take them down, especially when it comes to transmitting money..
That's why I do not support Zerocash. WIth Ring Signatures you can have full anonymity and still be Legal(so you're transaction history is still known by you incase of anything), while zerocash doesnt have such things.