The capped-profit / non-profit structure muddles that a little bit, but the reality is that entity can't survive without the funding that goes into the for-profit piece
And if current investors + would-be investors threaten to walk away, what can the board really do? They have no leverage.
Sounds like they really didn't "play the tape forward" and think this through...
But until he is re-hired Sam Altman is to all intents and purposes fired. And it may well come to that (and that would almost certainly require all those board members who voted for his ouster to vacate their positions because their little coup plan backfired and nobody is going to take the risk of that happening again, especially not in this way).