What is stopping any of the 1 billion Facebook users from using whatsapp, snapchat, or any other messaging service?

It's the inconvenience of having multiple accounts and logins with multiple services. Sure it's not as inconvenient as having multiple phone line accounts so AT&T customers can talk to Bell Atlantic customers but at the end of the day, your data is providing revenue to these companies and the companies continue to silo themselves.

Wouldn't that be easily solved if all the other services offered a "log in with Facebook" feature and routed messages to other people who also logged in with Facebook?

I assume there's a gaping flaw in this idea that I can't quite see at the moment ;-)

Part of the gaping flaw is that Facebook will very quickly disable your API account so you can't offer login with Facebook, if you're competing with them. :)

Don't forget that Whatsapp is also owned by Facebook