My terminal emulator (Konsole) has tabs. It also has tiling features I've never taken the habit to use. It has infinite history and allows me to easily select and copy paste many lines. It has a perfect scrolling behavior: it automatically scrolls, but stops auto scrolling if I scrolled a bit up. I'm used to its keyboard shortcuts to switch tabs. My window manager (KWin) also has tiling-like features when I need to see several terminal sessions at the same time.
I use screen when I need to be able to leave and rejoin later. I almost never need to restore several remote terminal sessions at once, and when I do, I'm happy to just ssh several times.
I feel like my use case is completely covered by the terminal emulator and the WM which are incredibly convenient and efficient. I would expect any layer between this efficient / optimized character display and the programs I run can only add latency. I also quickly feel overwhelmed by a screen full of characters. I think I would miss out on convenience by switching to tmux and it's unclear to me what I would gain.
Happy to be convinced otherwise, though :-)