They didn’t say it explicitly, but I wonder if their problem with screen time is that you can only "limit push notifications", you can’t "change the notification settings".

So if you have a work focus mode and want to receive work notifications only in that focus mode, you have to have the work notifications on permanently and when you don’t want to see them you need another "private" focus mode to turn them off otherwise. But they’ll still pile up, just slightly more hidden.

What I’d want is to actually change the notification settings of an app in a focus mode. So turn them on in one mode and have them off in another.