While I understand this sentiment, I think saying that you expect it to be scanning your entire computer is a bit of hyperbole. You expect it to be scanning your temporary internet files? Or DNS cache? Or your personal documents and pictures? I would expect those to be off-limits to a game library manager.
If you are saying that Steam was very upfront with its anti-cheat measures and that you agreed to it then so be it.
Steam provides a platform for a lot of developers and allows them to leverage the VAC. It's existence is improving our privacy. Instead of having each individual games try and scan our computers, they can call the VAC and request for the status of users.[1] When a game has a third party anti-cheat system, you can often choose to opt-out on install/launch and it simply cuts off online features.
This is one of the multiple reasons I don't mind Steam's scans. They are doing it on the behalf of thousands of games.
When people are worried about their privacy due to the VAC, they are quick to respond. Even better, they don't simply throw a legal team at the community but take the time to address fears and trust issues. [2]
I am not saying that Valve is perfect. They might mess up in the future. But so far, they have yet to breach my trust.