Herbsluft wm is less flexible than i3wm but I use it because of it. You can tile frames and frame can have multiple windows, with only few modes. No frames inside frames like in i3wm, I tried using qutebrowser without decorations and tabs. Each web page is separate window.
Only issue I am having is sorting of opened web pages. If you using only few web pages per virtual desktop it can be useful. With tabs in chrome you can move whole chrome to another tile or desktop. But if you have 20 qutebrowser windows it takes to long.
It doesn't solve frames in Emacs, or tmux/screen per se, but for tmux at least iTerm2 on OS X shows that doing a terminal emulator that integrates with it certainly is possible. For my part, my screen usage is very strictly "full screen" (or full terminal, I guess) so it flows relatively smoothly.
Sometimes it is annoying - splitting emacs frame and resizing it the same way as my tiles would be nice. Other times it is nice to be able to treat them on two separate levels. I'm not sure doing entirely away with the two level nature of that would be ideal.