I could be wrong, but I assume that Google mostly does this because of the huge amount of malicious garbage bot traffic on the web. Once you go fully anonymous and private, there's no way to distinguish you between the hordes of malicious traffic.

But there seems like there should be a technological solution. Google knows what a "legitimate" user looks like. Either because they come from a safe IP, or they're registered Google users, or they have a normal established browser history. But using your legitimate identify compromises your privacy, because then your IP/user-account can be correlated to your personal identity.

So, let's create zero-knowledge proof identity schemes. Using your legitimate, but non-private, identity you "register" an ephemeral, private anonymous identity. But it's done using zero-knowledge proof, such that Google has no idea about who a particular anonymous identity besides that it must belong to one of its several million legitimate identities.