" It might be a better solution where the ux designer/developer has some sort of button the website that then calls that function for a slightly better experience"

But this would be up to the websites then. They could do this now, but they aggressively push for all the permissions they can get in the hope at least some click (accidently) yes.

I do not want popups to click away all the time. I want to decide that I like notifications from site x if they offer that.