It always seems like you're on the side of the government, whether it's the NSA or what have you.
Often, yes. You see, I actually understand the design of the US government. It's built to continually revise and improve, and it's been doing so for over 200 years. On the other hand, your opinions have been forming for less than a century, and since you're only a single person, you've undergone far fewer revision cycles, all of which have been from a very limited perspective.
Also, any warrant asking to just search the entire house should be rejected, too.
Is that just, though? It may appeal to your sense of privacy, but would it appeal to your sense of justice to know that any criminal could effectively conceal evidence by simply putting it in a large enough box? How would your neighbors feel about it, knowing that you could be seen kidnapping their children, and the police could do nothing because they wouldn't know what room they're being held in?
Sure, the examples are hypothetical, but the underlying issue of deciding what is right predates your consideration by quite a long while. The best we have so far is a system where certain activities are absolutely permitted, and certain activities are absolutely forbidden, and deciding which category a given situation fits into falls to a judge whose primary interest is to bring the legal precedent closer to a state that everyone considers to be fair. It's not perfect, and likely will never be perfect, but it's closer than having Random Internet Guy simply decide that privacy trumps justice, because he says so.