You're ssh'd to a remote server and in a screen session. Actually, let's say you've got tmux going, and like four panes with different sessions to different hosts.
Now, you close your laptop, hop on your bike, enjoy a nice lunch somewhere, and head to a café for the afternoon. You open your laptop again.
Correct me if I'm wrong, but with your setup, you need to go to each pane and re-ssh to each host. But with mosh, I don't need to do anything except wait a few seconds. All of my connections are re-established, and (even without screen) my sessions are restored just as I left them.
That's almost as practical as keeping all your connections alive in a session, on a machine with a reliable network. Except that in my setup I can connect from any computer, while your is tied to only one.
I rarelly do anything like that anyway, because I don't like long standing connections. What are you doing with all those connections open anyway?
Configuring stuff? Why don't you clone your settings, and just push when done? (Or use puppy.)
Accessing local resources? Nope, if that was the case, losing the connection will disrupt your work anyway unless you script everything, in what case screen'll fit much better.
Waiting for a repply? Email and SMS are much better protocols for handling that.
Don't get me wrong. I see some value in automatically reconnecting to sessions (and when I care about a session, my computer does that). Also, handling bad connections (not intermitent) well is a feature. But those come at a cost - you are now tied to one client computer, and you can't script it as well as plain ssh, and some security concerns. I don't think it's worth that cost.
Now, you close your laptop, hop on your bike, enjoy a nice lunch somewhere, and head to a café for the afternoon. You open your laptop again.
Correct me if I'm wrong, but with your setup, you need to go to each pane and re-ssh to each host. But with mosh, I don't need to do anything except wait a few seconds. All of my connections are re-established, and (even without screen) my sessions are restored just as I left them.