You don't have to like it, but the global menu bar is at the top of the screen which means you just fling the mouse to the top and then go left or right, instead of having to get to the right vertical.

True. This could be nicely solved by placing a non-global window all the way at the top of the window, so that you can still fling the cursor to the top of the screen if the window is maximized or otherwise along the top edge of the screen.

I mean, it does take less space (compared to having one per window)

Only if you have two or more windows vertically stacked, which isn’t what you’re likely to be doing when you want to maximize vertical space.

but if they're stacked horizontally, buttons don't fit