It's an interesting question really, and it's not as simple as a binary choice. Fundamentally to have a functional society you need to have regulations, an authoritative hierarchy of some form (even if it's direct democracy) and a way to physically coerce those who do not obey rules.
The idea that this isn't a sacrifice of freedom would also be misleading, as it certainly is. When people say they won't sacrifice freedom I see it as just ignorant of the struggle and hardship required to establish the regulations that allow for an actual free society.
There's a very large body of political philosophy that disagrees with your fundamental assertion, though. Not everyone agrees with the Hobbesian notion of the state of permanent war in the lack of a State, or that such top-down authority is inevitable, even if they are acquainted with the argument in its favor.
In any case, that may make someone misguided, but not necessarily willing.
The idea that this isn't a sacrifice of freedom would also be misleading, as it certainly is. When people say they won't sacrifice freedom I see it as just ignorant of the struggle and hardship required to establish the regulations that allow for an actual free society.
I could go on for hours, but won't.