I was thinking about the same and I think the only way at the moment is for users to handle the notifications at all. If they switch off notification for x, they will most probably no longer get push notifications about that neither.

Sounds like a good idea to allow them to configure the push subscriptions. Currently they could unsubscribe from the notifications that pops up but I guess if there is a way that this could be integrated within the "Manage alerts" section, it would be nice.

Yes that would be great.

On the default onesignal script, they have a bell that appears on the page which users can click to switch notifications on and off.
Whilst it works well, my members complain that it gets in the way, especially on mobile sites.
Maybe there is some way to incorporate that concept into the Manage Alerts section?

Thanks for the input on this Marc, will log this into our internal issue tracker.