If I hide the menu bar, F10 doesn't open the menu at all. Since the F10 key can be enabled and disabled regardless on whether the menu bar was shown I would expect that it opened the menu temporarily when it was enabled even if the menu bar was hidden beforehand. Many apps do this (they just show the menu temporarily and let you choose an item or escape from the menu).
This is an interesting feature, but could you please name the apps that do this? For example, gnome-terminal works in the same way that xfce4-terminal.
In fact, I wasn't able to find any gtk app on my system that would show a hidden menubar when pressing F10. However, I came up with a change to show menubar if it was hidden and open the menu on pressing F10; but the menubar won't be hidden back automatically as it seems to be kind of tricky to implement. Do you like this behavior?
One that comes to my mind is Emacs. Another is Elinks, and anothers are Firefox and Thunderbird. I think I have seen this on more apps, but can't remember which ones. As for showing the menu bar but not hiding it afterwards I don't think this would be acceptable. The menu bar was hidden for something. I think the use case is the user doesn't want the menu bar to be shown but on some occasions may be interested in using, and for that (s)he uses F10. In that case hiding it afterwareds would be mandatory IMHO (at least it is for me, remaining there would make me not use F10).
Another from XFCE is Thunar. I'm sure there are many more.
I think you can look into Thunar's source code. It can't be that hard to implement and I'm sure you can translate that quite easily.
Thunar is behaving weirdly for me. If I hide the menubar and press F10, it will show the menubar which will stay. On consecutive F10 press, it will open the menu and then hide the menubar when I click somewhere outside the menu. I understand that if I could eliminate the first step i.e. show the menubar and open the menu on the same key press, it would suit you. I'll see what I can do.
Implemented by https://git.xfce.org/apps/xfce4-terminal/commit/?id=fd49cb660c333cb7534e15b3b759d1e202b489b0. F10 (if the shortcut is enabled) will now show and open a hidden menubar, and it will be hidden back once exited.