After using a tiling WM, it feels like this is a window manager job. It even works for non-terminal applications.

Except you don't need a multiplexer for that. Essentially all modern terminals have tabs. Many have split-screen. Even windows ships with a half-decent terminal with tabs and multiple panes by default now!

A multiplexer's job is to do the whole multiple tabs/panes/windows thing independently of the terminal itself, but (a) the UX for eg. tmux is so much worse than that of a good terminal UI, and (b) you only need that if you plan on connecting remotely (see my other comment https://news.ycombinator.com/item?id=49108483).