Saying "he has the option of separating himself from that stress" is true, but I don't think it captures the mental trap that people feel they are in. I also don't want to ascribe it to ego, because that has negative connotations. I think of it as a combination of not having an outside party to tell you to take some time, and working towards a goal with a single-minded focus.
Now I'm trying to do my own startup and its worse than ever. I'll probably go see a therapist in a week or so (when I get time!!!)
In my case, I'm unsure if having my advisor present would have made a difference. At that point, my work was almost completely self-driven - but that's rather the point of grad school. You're supposed to get to the point that you're calling the shots; the "authority" status of your advisor is supposed to diminish over time. But I'm also not convinced that having an absent authority figure is any different than not having one be design; I don't see how I would have acted any different if for some reason I had officially no longer had an advisor.
Having started a project that became successful for a time (though minute in comparison to Musk's projects) I can safely say that walking away when I had to was one of the hardest thing to do. There were people that counted on me, and they were really let down. It felt bad. And we're talking "fun internet community" not "future of the human race."
Being 'the boss' means you work to meet often unrealistic expectations you've set for yourself. It doesn't relieve you from stress, fear, deadlines.
Founders often perceive this feeling as a representation that they are the sole driver of the company's successes and failures. That means vacation represents a period of regression. It makes taking one essentially a nonstarter.
Worse, this behavior can be cyclical. Take a weekend off and you feel 'behind.'. Then you work twice as long next week, perceiving it as barely catching up. Then even harder to get back to the pace you thought you were on before.
Add to that the pressures of having billions of dollars and the livelihood of thousands resting on your expertise and the eyes of millions watching your every move ...
It's a hard habit to break. Even if you enjoy your job, the stress of what you believe it should be can add emotional and physical stress.
Even on a slightly less dire level -- CEOs have their employees and employees' families fate resting on their shoulders. It isn't easy to trust someone else to do it right. You can't just take a month off and hope everything goes ok.
When you have a moral imperative to work it isn't so easy as taking a vacation anytime you want.
That actually sounds like a messiah complex to me.
He will not be homeless next month, but he has personal debt the size of which could cause a small bank to fail that was used to fund Tesla and possibly SpaceX.
He will likely remain a very rich man, but at the moment his fortune is very much tied to the success of Tesla and SpaceX, so he also does not have as much freedom as one might expect.
If Elon Musk is stressed, he has the option of separating himself from that stress. He works because he wants to work. Employees suffer stress from which they cannot separate themselves without, in short order, creating new stresses. Elon will not be homeless next month if he stops going to work today. A psychologist might say that his stress is therefore a product of his ego, his daily choices, rather than of his environment. It is internal to his personality. That's probably why he finds it so hard to separate.