So what you're saying is that browsers already allow limited things like push notifications to happen silently without user consent, and this API just exposes the budget/cost for those actions? I'm not up-to-date on the background APIs that browsers expose, but this quote from the Google doc seems to be at odds with what you're saying, if I understand it correctly:
"The Push Messaging API enables us to send notifications to a user even when the browser is closed. [...] but the API has one important restriction: you must always display a notification for every single push message recieved."
And later:
"The Budget API, is a new API designed to allow developers to perform limited background work without notifying the user, such as silent push or performing a background fetch."
Edit: Reading through the spec more closely, it appears you are correct in that this is already happening on the browser side, and that this API just exposes the budgeting details to the developer. The Google Developer page's wording is just somewhat misleading. Thanks for the clarification.