She destroys the idea of meritocracy that she herself presented so eloquently and discredits libertarianism as yet another excuse for those born wealthy to keep their wealth.
If an hair is not equal to his money it destroys him? Come on, what does it even mean to be "equal to money"? And how can someone who does not inherit wealth even prove that he or she is "equal to the money"? That's just the kind of fluffy nonsense that moral philosophers are so infamous for.
As she argues, money is a means of trading human production and value. To be equal to your money is to provide production and value to society equal to the value of your money. According to Rand, if one who is barely capable of ever making more than $30k per year were to inherit $5m, it would not end well. And actually lottery statistics support this pretty consistently.
You don't seem to get what I'm saying at all. Among those who are willing and able to provide production value are some who get a boost from inherited wealth and some who do not.
Do you consider that fair or consistent with a merit based society? I do get perfectly well what Ayn Rand says in her books, and based on that her stance on inheritance is grotesque.
If you put all of this together, you end up with the person of achievement not caring where others started (or what they inherited) in relation to themselves. Fairness only holds value when the person getting shafted cares enough to give it value.
Besides, Rand's argument is that over the long run, it really doesn't matter, as the person who is capable of producing great wealth will do so, with or without an inheritance. The person who is not will quickly squander it all and end up right back where they started. Her point is simply that an inheritance does not change one's ability to produce.
A better analogy would be like saying that a king has a right to abolish his monarchy.
Also, it is only self-defeating if the original goal was only to amass the wealth.
To continue the analogy to this point, a king abolishing his monarchy would only be self-defeating if his only goal was to be a king. However, if his goal as king was to make life better for his country, then abolishing his monarchy in favor of a democracy would be a very good move and not self-defeating at all.
Likewise, if the person's original goal was to produce and then dispose of the rewards as he wished, then doing so is not self-defeating. It's only self-defeating if his original goal was to simply have wealth.
<edit> The other part of Rand's argument is that the individual has the right to dispose of their wealth however they please, because they produced it and they own it. A democracy would only have a right to dispose of itself provided it was the democracy that created itself in the first place. </edit>
Set theory is very useful but it needs an exception to survive Russel's paradox. You can't let useful things become useless just to uphold some moral rule.