Her valuable book (on which I am relying for much of the history in this column) also notes that the statue represented an expected “spiritual initiation to liberty” before crossing the border, and was seen as such at the time. The ancient Egyptians, Assyrians and Babylonians all regarded border crossing as an important ritual act, associated with “great spiritual changes.” The Statue of Liberty promoted a transformational and indeed partially mystical interpretation of assimilation.That's Tyler Cowen's Bloomberg column. He says, "We Americans tend to think of the statue as reflecting the glories of our national ideals, but that's not necessarily the case." Why not? Well, because the statue is like a sentinel challenging you and, as noted in the quote above, it was widely expected that people would change, that they would assimilate, by adopting the ideal of liberty when coming to the USA. It's telling that this absolutely reasonable expectation has come to be seen as contrary to national ideals.
The book Cowen refers to is Sentinel: The Unlikely Origins of the Statue of Liberty by Francesca Lidia Viano