This feature should never have existed. I used to work in a computer repair shop and saw hundreds of people with spam, scams, and malicious content piped directly to their computer. Most people have no idea how to make it stop, have no idea where it came from, but are aware it's happening and hate it.
Browser push is probably close to 100% malicious or ads at this point. It's directly enabled scammers to steal 10s of millions of dollars.
If Google came out with a feature that just stole $50 of iTunes gift cards from your granny no one would want it. That was browser push is at this point.