> No-one else provides anywhere near the same scale for free.
That's a bit naive. Google is not a charity and provides that service by making a profit out of user data.
> We don't send any personally identifiable information to Google. You are tracked by a randomly generated UUID (which you can regenerate at any time) and we tell Google to not store IP addresses.
Even with no IP, Google can easily cross-references searches and the random UUID, since a typical use case is that a user installs something through Homebrew after Googling it.
Please rethink this bad default choice. And sorry if my reply sounds harsh, but I think that Google tracking by default is an extremely bad choice for your users.