I agree that there are good cases for notification. It's difficult to find the correct amount of them and it's too easy to get so much of them so that everything important is being lost in the noise.

I don't know what's the correct balance is but for my own usage I'm ok using emails as a notifications spooler and only use native notifications for some specific usages (mostly chat and email clients). What's sure is that I don't care about notifications from my browser.

Btw I can only say for myself, we all have different way to use our tools. If your clients are happy with your notifications, great. I know I would disable them.