Rand is also grossly ignorant of (when not positively misinformed about) finance, business administration, industrial production, and legal philosophy and procedure, topics which presumably Rand's greatest admirers — members of the capitalist ruling class and professional-managerial middle class — have some degree of expertise or at least familiarity.
Most importantly, her incompetence as a novelist exceeds her deficiencies as a philosopher. (Ironically, Rand's primary goal was to become a novelist; the development of her philosophy was give substance and deep background to her novels.) Her prose is wooden, her characterizations one-dimensional, her plots implausible, she has no more feel for the details of verisimilitude as James Fenimore Cooper, and she clearly feels no more need for an editor than Stephen King. (The last criticism is not based only on the sheer length of her novels; the great 20th century epic writers, such as Michner and Clavell, succeed where Rand rails because they pack ten times more plot, characterization and verisimilitude in their own massive novels.)
I believe the two questions are related: Actual human beings care about Atlas Shrugged for the same reason that the characters in the novel are motivated to do what they do.
But the characters' motivation is indeed puzzling. One persistent theme in the novel is that none of the "good guys" are actually harmed by the system. Hank Rearden is a multi-millionaire and successful industrialist. His wife, Lillian, is a pain in his ass, but once he gets over his ludicrous uptightness and starts fucking Dagny Taggart, his wife fades into irrelevance. (The idea that either he or Dagny could be seriously socially or politically harmed by revelations of his infidelity or her fornication was weak in the 1940s when Rand began the novel, and implausible by its publication in 1957, and completely ridiculous when it became popular in the 1960s.) Late in the novel the government "robs" him of Rearden Metal, but he could just as easily have licensed its production to his considerable profit.
Similarly, Dagny Taggart is a successful executive, managing and operating Taggart Transcontinental, an enormous and critical industrial activity. She is able not only to operate her railroad, but successfully undertake a major capital improvement (laying new rail to Elias Wyatt's Colorado operations) even under the adverse conditions that ten years of John Galt's sabotage have created. Her brother, James, president and presumably majority stockholder, is again at best a pain in her ass, but she's clearly able to control him.
Francisco d'Anconia has apparently cornered the world market for copper. Ellis Wyatt runs a successful oil business (again during Galt's sabotage era) and is almost single-handedly responsible for the economic success of Colorado. Hugh Akston is a tenured academic and department head. Composer Richard Halley achieves artistic success and recognition before joining the strike. Midas Mulligan is a successful banker (who has apparently never heard of the appellate court). Even Cherryl Brooks has achieved considerable material success by marrying James Taggart.
John Galt himself, a preternaturally brilliant scientist and engineer, is only mildly inconvenienced by the "communist" takeover of the Twentieth Century Motor Company. The new legitimate management is admittedly not to his taste, but he is free to leave and manages to take his intellectual property with him. (And he is extraordinarily naive or stupid if he cannot figure out a way to profit by his talents even if her were to cede his intellectual property to the TCMC.)
Indeed, Rand portrays all of the "strikers" as not just responsible and productive, but also economically and socially successful. Actual success appears to be just as much a criterion as responsibility or productivity. "Atlas" may be holding up the world, but he appears to be well compensated for doing so.
Rand's in something of a philosophical bind, a bind that squeezes all deontic ethical philosophers. On the one hand, she's making a case for the inherent (deontic) worth of certain values; on the other hand, she has to show the pragmatic* worth of those values. She can't have her characters be largely unsuccessful in ordinary society; her entire philosophy would then just sound like sour grapes. But if they are successful, what precisely is their complaint?
*Note that expediency and most unappealing "ends justify the means" ethical philosophies typically restrict the range of pragmatic consequences that apply to ethical evaluation; when they fail, they fail because of their restrictions, not because of pragmatism in general.
The stated reason for the strike is of course that other people have the "wrong sort of values". But so what? John Galt is not actually harmed by the TCMC (and the company predictably goes bankrupt on its own due to management far more incompetent than any seen in the Soviet Union). Midas Mulligan might have to make one or two bad loans to incompetents, but the legal system has never been perfect. Hank Rearden could easily divorce Lillian, and even if he pays alimony, he's hardly going to be reduced to living in a mud hut living on beans and rice. Hank could also tell his ungrateful brother to STFU and GTFO (which he finally does), or just shrug off Philip's and his mother's contempt and resentment with amused indifference.
Indeed Rand portrays those with the "wrong" values as so ludicrously incompetent and self-defeating that it is only Galt's strike that gives them the capability to actually mismanage the world. Absent the strike, they are already marginalized and ineffective. How does Rand successfully elevate the condition of people who have already achieved success as an epic struggle against oppression?
Likewise, Rand is most popular among the middle and higher levels of the professional-managerial middle class, and the lower levels of the capitalist ruling class (as noted above, these classes overlap considerably). You won't find a lot of workers reading Atlas Shrugged on the factory floor. The exclusively white characters don't have much appeal among ethic minorities. Rand is hardly a feminist icon. Again: what is the appeal of Rand's epic struggle against oppression among those who are obviously the least oppressed: ruling-class (or near-ruling-class) white males?