poor mouse support
Well, not to be too snarky but you _are_ running screen/tmux in a terminal window.And I hope I'm not the only person who considers having to move my hand off the keyboard and onto the mouse a UX bug.
every command you send to it has to first be announced
with a prefix keystroke
A friend of mine revolutionized my life when he showed me how he'd remapped GNU screen's command key from Control-A to backquote (`). Using screen went from being moderately annoying---especially to a die-hard Emacs user like myself---to being an essential part of every Unix/Linux server install I have done since. To be honest I don't understand why screen and tmux don't default to backquote instead of Control-A/Control-B, but maybe that's just the twenty-plus years of Unix-induced brain damage talking. :)