Yes there are other solutions that don't require Google to know who your favourite team is, but needing to have your device run a specific background process to constantly poll a remote server for each of the things you're interested in is a pretty clunky and resource-inefficient way of solving it vs subscribed push notifications from the server.

And Google doesn't necessarily know that you like $team. It knows that the email address you used to sign up to the alerts has requested updates on it. Is that really particularly scary?