Admit it. That's a draw.
This is handled by title bars in Gnome, OS X and Windows, not window menu bars.
"separates the data (what's inside the window) from the menus that act on that data"
The menus don't just act on what's in the window. At least some menu items act on the application itself.
In a multiple document interface with a system that ties menus to windows, the menu of one window acts on multiple other windows. The other windows are either sub windows shoved inside the main window or they are windows floating independently from the window with the menu, which means you need to return focus to the main window to use the menu.
In a single document interfaces, the same menu, application controls and all, is repeated on each individual window.
Furthermore, in both of those cases, once you close the window with the menu bar, you no longer have access to any controls for the application, which is why most applications in these windowing systems can't run without at least one window open.
As opposed to "application buildup" MacOS users experience since the OS7 days, when they are on a clean desktop and five applications running for no particular reason.