Most libertarians are not "anarcho-libertarian", whatever that actually means, nor are we anarchists.
I think most of us agree that a state is important. The question, which people have been grappling with as long as there have been states, is how to make sure that the state is benevolent--that it actually works in ordinary people's favor, rather than degenerating into a relationship of oppression and exploitation.
The libertarian question, specifically, is how do you ensure that the state respects people's individual freedoms?
History has shown mass surveillance to be antithetical to individual freedom. So our goal is to abolish mass surveillance.
You said we're "so coddled by the benefits of a first-world government". Do you think MLK was coddled by his gov't when he was hounded by the FBI, sent threats, & imprisoned for his words? We are lucky that the surveillance capabilities of the state back then were much more limited than they are today.
Today, every email in your inbox, every text, every cell phone GPS coordinate, every draft in your drafts folder is plaintext in a big database. That database is searchable by bureaucrats you'll never meet. Even if they never type in "rayiner" specifically, this state of affairs is dangerous to the freedom we all enjoy. Just because we have it better than some unlucky people elsewhere, doesn't mean that we should stop trying to fix our own society here and now.