Security over Freedom?

That entirely depends on how you define "freedom". Even you are in a cage, you aren't free, but are you free even if you aren't in a physical cage? You are still enslaved to a system you are within. Say you tear down that system and the world fall into anarchy, are you free? Even if you are still following the rules and laws given to you by time? You can talk about destiny and so on in the context of freedom for quite some time. I personally think that freedom is the ability to chose a path of your own accord even if the system, the world or even a God tells you that you can't. Freedom isn't the ability to defy everything that isn't you, it isn't the ability to redefine the world for others or to even affect the world for others. It is the power to follow what you believe in.

Thus a government system can't really take that away unless you give that right to them or if we reach a level of control where people's brains are taken over through outside means from birth. (No, I am not talking about brainwashing, as you are still you, just influenced). So as it currently stands, a government can't and wouldn't do that. So yes, I would trade my ability to keep my Google Search History private for the perks that I get for doing so.