First, remember that you only need to click 'Yes' when your browser asks you for Push permission. You have revealed nothing new to the website, but provided it a way to contact you later. Think of it as a frictionless temporary e-mail.
So you go to a ticket website, or maybe its even a restaurant website, and there's some event coming up. Huh, yea, you want to know when tickets go on sale or whatever, but no way you want to give out your e-mail address again and get all that spam.
You instead opt for a push notification from the site when the tickets go on sale. Now you will be notified via your browser, and maybe once you see that notification, you're happy, you're done, so you unsubscribe (an option you can click on the notification itself to stop further push messages from that website).
If this privilege is abused, just as easy to cut-off that sole way to communicate that it has with you, right there on the notification. Unlike e-mail, when you kill the Push permission for a site, it has truly lost the ability to bug you ever again.
I'm sure there's plenty of other cases where it might be useful to one-off contact a user when they want to know about something your website provides, and people are (properly) wary about giving out e-mail addresses.
One of the nice features of Web Push notifications is that they each have an unsubscribe button on the notification itself. So once you don't want to get them from a website anymore, the block button is immediately available.
Just visit the site, get an infinite session, and voila!
Logging in from a different machine? Cleared cookies? No problemo - to restore your session, get a notification, click it and session restored!
This is the poor man's "iCloud" also. Basically your google login or firefox login is your master login. It's basically same facebook connect - another identity provider. Move over personas! We've got a new OpenID in town. Except instead of email providers it's the browser vendors.
NOTE: This doesn't solve the problem of power dynamics -- browser vendors are still pretty centralized -- but does make it super simple to let users of these browsers get a account on a site without an email, mobile number or password, at least on the desktop.
facebook.com forums.meteor.com
I find them useful.