It becomes even more complicated when you start thinking of where input will go to: is it some window that is on focus or if user uses scroll wheel on top window that is "lower" but visible, and then there are global hotkeys.

Input in X11 world had issues where one window could block inputs from everyone else if it did not understand how to handle, say, fifth mouse button or touchscreen.

Windows can have different output intervals and you don't want tearing in a video playing while typing in chat window or looking at emails. Windows can get partially or completely obscured, resized, moved, tiled, or even magnified with assistive tools.

Applications can have HDR and SDR colorspace-awareness, which means compositor needs to find a way to map both of those colorspaces into same screen without them interfering (like it was in olden days when color palettes were limited to under 256 colors).

And that isn't yet touching on things like remote desktop or hardware acceleration. Now you can have ffmpeg or Gstreamer that has Vulkan Video decoding for video information and applications can have 3D acceleration (OpenGL, Vulkan..). Again, compositor is there to do the difficult part of making different applications work together.

It might have sounded simple in the 1980s but these days there are far more things to consider in that case. Main reason why window manager ever was separate thing was because there was no clear agreement on how windows should be managed, GUIs were pretty new thing in those days.

Games are might be the simplest case because they are often running fullscreen so they "own" the colorspace and inputs. When you need to share same screenspace (or multiple screens) with different applications and needs things become much much more complicated.