Well, OK, continued existence is one (the only?) of her moral axioms. The statement "the continuance of good existence" implies that there is some other moral axiom at work as well, which quantifies or qualifies the state of existence. What would that be? - In any case, you are getting to the heart of her (arbitrary) morality.
Yendu's opinion about that thought .... In any case, you are getting to the heart of her (arbitrary) morality.
Descsrtes' use of reason to derive "I think, therefore I exist," has come in handy in my possible derivation of the truth underlying Rand's rational ethics. The term, "I exist" leads to the fundamental question as to whether human existence is good or bad; and it can be bad for those near death. But continued existence, however temporal it may be, is by far preferable -- the good -- to most humans. And that connection to "the good," being an essential element in matters ethical, leads to the defining thought that ... "my ethics is concerned with the continuance of good existence."
Given that rational thinking, what is more arbitrary; truth derived from reason or dogma emanating from individuals that people (even millions of people) have faith in?
A further note about Descartes ... His "Meditations on First Philosophy" was published and then placed on the Roman Church's Index of Prohibited Books, but Descartes withheld his work on Physics, entitled "The World," when he was told of the Inquisition's persecution of Galileo for supporting the Copernican theory -- Descartes's work contained similar ideas.
One possible (I'm relying on distant memory so corrections are welcomed) irony regarding Galileo and Copernicus, is that both are now entombed in a tourist oriented "must see" Catholic church in either Rome or Florence.