>> Under what circumstances would one want to receive these sorts of messages over a Facebook message instead of via email?
If you're the kind of person who instead asks "Under what circumstances would one want to receive these sorts of messages via email instead of over a Facebook message?"
I'm 28 and I have a 50/50 mix of people using Facebook messenger just like a SMS. It's definitely a shift that is happening in people's comfort level with social media as a primary comm channel.
29, my parents and their friends 60, 70+ all use whatsapp instead of SMS. Whatsapp, Messenger, Google Talk, even Jabber… With modern smartphones it's all the same, the only difference is who's on what which is why I hated when everyone moved away from XMPP.
19, it's like 30/70 SMS/Facebook in my experience. (Then there's Snapchat, but that is more of an overlap than a replacement.) I think part of it is that Messenger handles groups well and everyone is on it without needing a number.
Frankly I hardly use Facebook-the-social-network much, but I use Messenger all the time.