tl;dr: Integrating you mail client into the browser doesn’t really give you much.

IMHO it’s also a bad idea. I want my browser and communication tool separated on purpose (if I don’t open any of those as a website anyways).

Not the first browser doing that. Probably not the last either. But none of them caught on. It’s not a feature anyone wants or needs.

Most browsers used to have email. Seamonkey, Opera, Netscape Navigator, etc. While I have nothing against them I don’t use them very often, although Seamonkey is still around and is great for running from USB sticks.