You are a two factor app. I should never be in a situation where there is an unexpected login I need to verify.
I know lots of apps behave badly when it comes to notifications but I'd still prefer if the apps controlled the level of notifications they sent. I could, of course, reduce that client-side, but I don't see why I'd want Google or Apple or any other intermediary see or control the notifications.
If an app behaves inappropriately, I could uninstall it. If a gatekeeper like Google or Apple prevent an app from sending me notifications, I'd have to change my OS, usually my hardware, too.