I believe it's because most (if not all) of the mission's menus cut most of the mouse and keyboard input while they're displayed. Partly this is done to stop people opening menus while running around or driving (because that would be a tad silly and dangerous) and partly it's so that the menu can be sure of trapping any inputs and directing them to the menu, not the game.
I have (for a long time) toyed with the idea of whether to allow things like the VON transmit key to be useable while in a menu (how many times does a cop get popped because he's stuck in a ticketing or vehicle-registration-check menu and a player is getting edgy? Too many). But it is a bit of a minefield. It opens up various exploit possibilities that I will not go into here.
I may yet find a safe way, though.
But it does beg the question... why would you want to be doing 'RP housekeeping' whilst flying? It's a tad dangerous, no?
Not intentionally - at least, not by me... but goodness knows what's in there from before. I'll have a look sometime and see whether there's anything that might do that.