My apologies, the last time I used safari as my main browser was in 2014. This is the first time I see the notification and I thought it could be useful. In my mind I thought you would only get the notification rarely after hours of using a website like Twitter. It could definitely get annoying if it's a common occurrence, especially on a PDFs.
As for an alternative, beside what szlend suggests, I'm not sure what else could be done. But even that, there are many people that don't like having a notification/badge anywhere on their screen so I could see how this also can be annoying.