The problem comes when the situations starts to resemble the line about how, if you owe a bank a billion dollars, you own the bank: if the direction the CEO has taken the company differs enough from the vision of the board, and they've had enough time to develop the company in that direction, they can kinda hold the organization hostage. Yes, the company isn't what the board really wanted it to be, but it's still worth a bajillion dollars: completely unwinding it and starting over is unthinkable, but all the options that include firing the CEO (the only real lever the board has, the foundation of all the decision-making weight that they have, remember) end up looking like that.
It does not matter that the board has the legal power to do whatever they want eg fire the CEO. If the investors and key employees that keep the company going walk away, they end up with nothing so they might as well resign and preserve the organization rather than burn the whole thing down.