The assumption is that such an algorithm already exists because of windows managers but it seems like a fun diversion.

Is it? I gladly admit I don't know most window managers, but the few I haved used only place one window at a time - they don't seem to be confronted with the problem of placing many windows at once. Furthermore, it's usually not up to the window manager to determine how large a window should be; it's the application that asks "please mister window manager, I've a window of this size, would you please put this on the screen?"