Photo by J Scott Shannon.
The main reason I have my doubts about this is that, back in the '00s, '10s and '20s, when there were lots of people around who should know the correct, original spelling, the appellation is apostrophized more often than not; as either "Angel's" or "Angels'." It seems to me that the apostrophized spelling only fell out of favor after the 1920s, when the The Benevolent and Protective Order of Elks erected the massive filigreed archway that today is the landmark's signature. There is no apostrophe to be found on this monument. But should there be, in actual fact? I do wonder...
So, can someone maybe produce, say, a copy of the architect's/builder's original plans that would prove their intent to either apostrophize or not apostrophize the railway's name? Or perhaps there was an official program printed for the dedication of the railway in 1901 that would settle this spelling question once and for all. Even a good, close-up photo of the original archway should do.
Until I see proof one way or another, I will continue to abstain from using apostrophes when I spell "Angels Flight," but I remain quite curious about just exactly how the name should properly be punctuated....or not, as the case may be.