There's many non-tiling WMs that actually manage the windows for you:
http://fvwm.org/documentation/faq/#when-my-specific-window-o...
Ah, fvwm. Now thats an old war horse of a window manager. And it is still maintained no less.
I do wonder if anything Wayland related will have such staying power.
It's indeed actively maintained!... lots of changes and updates recently. They're cleaning up the code base.
After using it for over 12 years, I'm still amazed just how incredibly flexible fvwm is. You can even mimic tiling with a bit of effort (see here: https://www.youtube.com/watch?v=xdSgf-IykIo ).
The tiling part of it isn't the important bit: what's important is that they keep your windows placed in a useful manner for the task you're performing, tiling in various ways being one of the ways in which they achieve that.
Normal window managers are akin to a desk where everything is tossed around, whereas tiling window managers are like desks that automatically organise whatever is on them.