Collecting telemetry is reasonably, but it seems inappropriate for Google to get a copy and to be able to identify which of their users installed a particular piece of software from the IP address.
So yes. Running their own server would be much preferable.
It's worth noting that AIP's functionality requires you to trust Google -- the data is received by them, but their design specifies that they mask it before it's processed or stored.
While I feel we should all treat Google with skepticism here, I didn't realize they (and so failed to acknowledge) that Homebrew was attempting to remedy that, so I apologize for speaking out of turn.
So yes. Running their own server would be much preferable.