The exact scenario you're describing is a great use case for tiling WMs. I couldn't imagine doing it with windows that occlude each other. In fact, I've been using tiling WMs for over a decade now, and I find my colleagues' use of stacked windows gives me anxiety. You never know where anything is, and they have to constantly alt-tab to find it, or hunt for it with their mouse.

The key to effective use of tiling window management is the use of virtual desktops. The two go hand in hand. That's why Windows and Mac OS don't have it. Windows, btw, did re-introduce a "tiling mode" (or something like it) in their recent OSes. The use case to have two windows next to each other without fiddling with your mouse is just so prominent.

I rarely have more than 2-3 windows per desktop. The browser usually dominates its space completely, and is full-screen, almost always.

EDIT: I know Mac OS has "virtual desktops" now, but in the grand scheme of things, it's a relatively recent addition, and I doubt that many people use it. It's probably more of a power-user feature. But then again, so is tiling window management.