I actually implemented a system very much like this on an internal company network recently. For that purpose, it worked great. I don't think it would work in an open, public context, not least because an attacker can force your site to spam its users. However, when you are going to stay logged in forever on basically the same devices, having an email-based login system without a password is no more pain for the user than a verification email (since that's all you're doing anyway). Essentially you're relying on the website to generate a local, device-specific, secure password instead of requiring the user to create and remember a (likely insecure) password themselves.
