This bugs me too, especially as a long time Mac user. Luckily, I’ve had good luck with the HTitle extension to hide Firefox’s titlebar.
It’s designed to work with Gnome Shell, and I’ve had trouble with non-mutter-based window managers, such is Xfce’s wm, but it seems to work fine with Mate. (Maybe because of the shared ancestry of Mate’s wm and mutter?).
(I also use a vertical panel to save more vertical screen real estate – in fact, this option is one reason I first started using Mate – but that’s another topic.)