Now it's going to be much harder to send messages from your friend's phone when your phone dies. Before you could use an incognito tab, and now you have to log out of the Messenger app entirely and log in as another user.
Thank you for bringing up this point - I've often thought about it before, but I didn't immediately think of the connection here. Just another reason why these kinds of changes are a bad idea. It might not be that often that you're without your device (battery died, stolen, forgotten), but when that happens not having a great fallback is really annoying. This goes for all kinds of apps and services, not just fb messaging.
It doesn't seem like you can even log out anymore inside the iOS Messenger app. My wife was without her phone a few weeks ago and needed to message someone via FB.
I could not find the log out button in iOS Messenger, and the only way to do that seems to be logging in to fb.com and hitting a button there which will deactivate your phone session.