Another user commented that you could just register your own domain and do this; that's great for the average hacker news reader, but not so great for the average Joe so a service like this (if done correctly) would be pretty convenient.
Things that jump out right away as bad about this NBox.
1) It just auto generates an email for me. That's going to be a pain in the ass to remember.
2) Wait; how do I login? I literally don't understand how to login to this app short of going to the site and I get auto logged in by the Chrome extension?
3) Why do I even need a Chrome extension to get my email; where is the password protection so I can login from a different device or god forbid my computer crashes?
4) Not every service asking for an email address is a web service. If I sit down for dinner at an Applebees and order a meal a server is going to tell me the appetizer is free if I just provide my email address... and I want that free appetizer minus the side of spam...
As someone else noted mailhero.io is basically the same service as this, but it's big flaw is that the real email address is exposed since it's always included in the provided email address.
spam.u.later@mailhero.io (ah; real address is later@mailhero.io) Also; many other email services (including GMail can do the samething as mailhero using + addressing and adding rules.