I separated this to address some points on Rand's philosophy and how it plays out, that I think you misrepresent.
You wrote, "Property rights being the basis of all other liberties." On the contrary, she argues in great detail in her non-fiction (but more implicitly in Atlas) that a) liberty precludes property rights but is nothing without them and b) the individual, volitional, mind precludes liberty and is of little use to the individual without that liberty. That is, Man by his nature is a conceptual being who is designed to evaluate the physical world and to choose to act according to how he sees it. The removal of liberty to act on his thoughts negates his nature as Man. Similarly a Man is a physical being with the moral requirement to look after his physical existence rather than parasitize others (he is not an ant or bee in a hive), so those things he accrues for the task of maintaining his existence must be viewed as his property. The Rights to Life, Liberty and Property are closely intertwined, but they have a definite hierarchy that begins with a Man's life and mind.
You wrote, "Rand's theory very quickly leads to power-imbalances that would quickly see the entire world reduced to a rich-poor ratio that would make the slums of Mexico City seem a marvel of social and economic equality." By that argument, once slavery was abolished (thanks to the spread of the ideas of the Founders and their U.S. Constitution's effort to enshrine Life, Liberty and Property for every Man) the U.S. should have degenerated into the very scenario you named. It did not. The slum dwellers of, say, Pittsburgh, had TV's and cars (they should have forgone the TV to get health insurance), while the slum dwellers of other, non-capitalist countries had to beg for food and slept on the streets. People were not immigrating to Mexico, they were immigrating to New York. Rand understood. I contest that a lot more Americans should understand their own country a lot better (I am a Canadian who understands it, and have enough experience with our own socialism to resent it. You guys do NOT want socialized medicine; your Medicare, Medicaid and outrageous litigism against doctors have already driven up your costs and are harming you. More of the same is no solution.)
You wrote, that the successful corporate leader will, "...find himself with a monopoly in his field and a strangle-hold on his labor force." This is a myth promoted by socialists. No monopoly is secure in a free country. If Bill Gate's Microsoft actually achieved a monopoly by buying out Apple etc. what is to stop GMC or even Honda (both of whom use non-Microsoft compatible software in their vehicles and factories) from seeing an opportunity to compete? Indeed, should 'Bill' gouge his customers too much, potential competitors will seize the opportunity. Likely, they will have innovative ideas, while 'Bill's' bureaucratic behemoth will have (has?) become too stagnant to rise to meet the newcomers. This principle applies to all so-called monopolies, but when legislation interferes with certain markets (laws that require certain standards be met) newcomers have a much more difficult time entering that market, because they have to dedicate limited resources to meeting laws, rather than the customers that appreciate what they offer. Government interference actually helps ensure that monopolies, or a few large corporations, exclude those newcomers.
RnBram
I separated this to address some points on Rand's philosophy and how it plays out, that I think you misrepresent.
You wrote, "Property rights being the basis of all other liberties."
On the contrary, she argues in great detail in her non-fiction (but more implicitly in Atlas) that a) liberty precludes property rights but is nothing without them and b) the individual, volitional, mind precludes liberty and is of little use to the individual without that liberty. That is, Man by his nature is a conceptual being who is designed to evaluate the physical world and to choose to act according to how he sees it. The removal of liberty to act on his thoughts negates his nature as Man. Similarly a Man is a physical being with the moral requirement to look after his physical existence rather than parasitize others (he is not an ant or bee in a hive), so those things he accrues for the task of maintaining his existence must be viewed as his property. The Rights to Life, Liberty and Property are closely intertwined, but they have a definite hierarchy that begins with a Man's life and mind.
You wrote, "Rand's theory very quickly leads to power-imbalances that would quickly see the entire world reduced to a rich-poor ratio that would make the slums of Mexico City seem a marvel of social and economic equality."
By that argument, once slavery was abolished (thanks to the spread of the ideas of the Founders and their U.S. Constitution's effort to enshrine Life, Liberty and Property for every Man) the U.S. should have degenerated into the very scenario you named. It did not. The slum dwellers of, say, Pittsburgh, had TV's and cars (they should have forgone the TV to get health insurance), while the slum dwellers of other, non-capitalist countries had to beg for food and slept on the streets. People were not immigrating to Mexico, they were immigrating to New York. Rand understood. I contest that a lot more Americans should understand their own country a lot better (I am a Canadian who understands it, and have enough experience with our own socialism to resent it. You guys do NOT want socialized medicine; your Medicare, Medicaid and outrageous litigism against doctors have already driven up your costs and are harming you. More of the same is no solution.)
You wrote, that the successful corporate leader will, "...find himself with a monopoly in his field and a strangle-hold on his labor force."
This is a myth promoted by socialists. No monopoly is secure in a free country. If Bill Gate's Microsoft actually achieved a monopoly by buying out Apple etc. what is to stop GMC or even Honda (both of whom use non-Microsoft compatible software in their vehicles and factories) from seeing an opportunity to compete? Indeed, should 'Bill' gouge his customers too much, potential competitors will seize the opportunity. Likely, they will have innovative ideas, while 'Bill's' bureaucratic behemoth will have (has?) become too stagnant to rise to meet the newcomers. This principle applies to all so-called monopolies, but when legislation interferes with certain markets (laws that require certain standards be met) newcomers have a much more difficult time entering that market, because they have to dedicate limited resources to meeting laws, rather than the customers that appreciate what they offer. Government interference actually helps ensure that monopolies, or a few large corporations, exclude those newcomers.