Push notifications in Safari just suck because the discoverability method is a dialogue box that interrupts and blocks all other user actions.
The browser should never let a website interrupt unless allowed by the user. Place a bell icon in the address bar and make it translucently balloon up when triggered for visibility.
Side note: Browser interface should stay outside the untrusted zone of web content. Whenever it can't, interface could have an unobtrusive unimitable background pattern extending from the trusted zone into the untrusted zone. The user should always know what is browser or website.
The browser should never let a website interrupt unless allowed by the user. Place a bell icon in the address bar and make it translucently balloon up when triggered for visibility.
Side note: Browser interface should stay outside the untrusted zone of web content. Whenever it can't, interface could have an unobtrusive unimitable background pattern extending from the trusted zone into the untrusted zone. The user should always know what is browser or website.