There's some elements that remind me of Moped (http://blog.moped.com), which has since been bought and shut-down. It's actually quite more enjoyable to keep this stuff out of your inbox, and if you really wanted to, you could use Moped as your email client. I don't use Hangouts, but doesn't that require other people you send messages to to also have Hangouts etc?
Disclaimer: I wrote the Mac client for Moped.