Because not every manager is, nor needs to be, Windows?
Prior to the green button gaining the fullscreen functionality, it used to toggle between two sizes: (A) a developer-determined default size and (B) as large as the window needs to be to accommodate the content at the content's current zoom level.
This is inherited from macOS' days as NeXTSTEP, since the "global menu bar" was originally a floating palette window whose submenus could be detached and float, too. If windows were allowed to fill the screen, they would have blocked access to the menus. So, windows were made only as large as necessary, no more than that.
To me, macOS' behaviour always made more sense. Why should a window need to be bigger than its content? Drives me nuts to see 27" diagonal displays with huge Chrome windows showing a column of text about 6" wide and then the remainder is just white space.
It feels like Microsoft cottoned on to that with its Aero Snap feature in Windows 7 that far too few people actually use. So much wasted screen real estate.
> Why on earth would the green arrows button do anything except fill the desktop with the window?
That's exactly what they do. You click the green button, it fills the screen with a window.