I think you are spot on with your reasons for why these things actually do exist, but I think there is definitely an argument to be made for why they should act

I think you are spot on with your reasons for why these things actually do exist, but I think there is definitely an argument to be made for why they should actually protect privacy instead of merely inhibiting the government. My version of the argument goes something like this: It's often said that drivers (in the US anyway) are constantly violating minor traffic laws, and that if the police want to pull someone over, all they have to do is follow them for long enough and they will find a legitimate reason to do so. I believe that this extends far beyond the sphere of traffic. I think we all accidentally break minor laws way more often than we think we do. We all way overestimate how "good" we are. If it was possible to automatically punish everyone for every violation of the law, we would quickly realize that many laws aren't actually that important, that they can be broken a little bit, constantly, by basically everyone, and society still functions just fine, and that privacy is more important than perfect enforcement of law. Of course this might lead to a new equilibrium where we perfectly enforce a smaller set of laws. All this is to say that I think people think they value law enforcement more than privacy, but if they had the full force of the law brought down on them for every minor violation, they would quickly change their mind. In that way, privacy (in the form of the government not having perfect information) is actually quite valuable.