Nobody would notice or care what happened to John Galt, because the world runs perfectly well without a rich douchebag telling it what to do.
And within about a week, he'd be dead, because rich douchebags like him are so used to people doing things like washing their clothes, cooking their food, and cleaning their houses that they wouldn't know what to do without them.
The book appeals to rich douchebags because it validates their egotism: "Of course I'm harder-working, smarter, and more important than everyone else! Otherwise, how would I have gotten so rich? I should be allowed to do exactly what I want, and answer to nobody but other rich people, because civilization depends on me."
When in fact, they depend on millions of people that they don't even notice. Their whole existence is an exercise in ignoring all the people that enable their lifestyle, and the people best suited to do that are not the brilliant, but the sociopathic. And in fact, when you look at the actual plot of the story, John Galt fits the part perfectly--his primary goal is to destroy human civilization as punishment for not recognizing his achievements, and he's presented as the hero. Ayn Rand has a lot to answer for.