Shouldn't the law prevent the CEO from doing just that? I mean, the board is presumably the only check on the CEO's power, so even if the CEO is the majority shareholder, they shouldn't be able to control the board.
But yes, as the controlling shareholder, you can fire the board. That's what being the controlling shareholder means; the one and (basically, only) thing you get to do is appoint a board to run your company on your behalf. And you can keep firing the board until you find some lackeys who will agree to do whatever you want, including hiring you in any position you care to to name, including, why not, the CEO role. That's totally legit.
If what you want harms the minority shareholders, then they can sue, and depending on the details, they'll have a great change of winning. CBS and Viacom are currently working through this right now; the controlling shareholder wants to ram through a merger, and the CBS board thinks it's a bad idea. Under pretty settled law, she can fire the board in revenge, but if the merger is actually bad (and the fact that the current board found it so is strong evidence that it might be), then she can't just replace the board with people who will agree to it.
> the board is presumably the only check on the CEO's power
The board is there to look after shareholders. If they fail, then lawsuits from shareholders are the final check on CEO power. That doesn't change much just because the CEO is the controlling shareholder.
What's the worst they could do? It's their company. Worst case the CEO runs it into the ground and everyone loses their money.
CEO =/= President of the United States.
If it was YOUR business, you would want to control your dream, your vision -- not a bunch of rich folks who could decide to kick you out from your dream if your main goal is not to _remain profitable to the shareholders_.