I'm not suggesting the board actually did anything legally risky here. The standards for that in Delaware are high. But morally, it's much harder to defend, so long as they knew this is what the outcome would be --- which it seems like they kind of clearly did.
On the other hand, if you're arguing that a board should be able to fire the CEO without cause and have him barred for eternity, then you're arguing that majority shareholders shouldn't be allowed to serve as CEO - in a private company !! - which has been the basis of capitalism for ever. It would destroy the economy as we know it.
That doesn't mean they're required to faithfully represent the interests of any one person with majority voting power, but it does mean they can't select some random subset of minority voters and serve them instead.
It's the people they represent, i.e. the shareholders, who get to decide what's the good of the company, and the board is simply meant to enact those wishes. This is a constitutional issue of representation: at what point do the elected representatives decide the current situation calls for a referendum instead of an ordinary (representative) vote ?
> The majority shareholder says jump off a cliff and we must obey” is nonsense
If the majority shareholder decides that, then 1) the board must resign at once and 2) any one minority shareholder must sue and have the Delaware Court of Chancery determine that the majority shareholder has abused his powers. I'm not sure what would follow that court decision.