Terraforming Mars does something very similar. One problem my friends and I discovered with this approach was that it was possible for multiple people to hit the button that started the game at the same time (it took quite a few seconds to process the command and then hide that button from other players), and that would cause complete havoc (although a simple Undo always seemed to fix things). So, I ended up modifying the Start button action so that it would only respond to a single player (the one who started the game).
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