Character delay is absolutely a real issue over mobile network connections. I will occasionally try to get some work done on my laptop during a car or bus ride, tethered to my phone.

And while tmux/screen do keep the state server side, so you can reconnect, you have to do it manually. I usually connect to the wired network at my desk (to get lower latencies using Synergy), but may unplug my laptop to go to a meeting or debug an issue at another desk. Having to re-establish all of my connections when I do that is a pain.

And finally, tmux/screen do nothing about the UTF-8 incompatibility situation, and in fact may make it worse by adding an extra layer in between in which encoding information can be lost (I haven't played with this very extensively, but I have been frustrated in the past trying to get UTF-8 text entry to work over SSH).