I think that reading the story as an allegory is not successful, for precisely the reasons you give. For me, the book was more about the thought experiment; I agree that the 2 city arrangement was alien. Yet for me what was great about the book was not the plot - essentially, a pretty run-of-the-mill detective story - but rather, forcing myself to adapt my imagine the reality of the city. I think perhaps this works better in text form than audio form, as text allowed me to take the time I needed to get used to the concepts, and reread whenever I wasn't sure things were internally consistent (they always were, as far as I could tell). Audio, where pausing and rewinding feels a lot less natural - and there is no way to just stop and stare at text for a few seconds until it sinks in - would probably have made the experience a lot weaker.
And contra all that, there is one other factor for me. I grew up in Jerusalem, very much multiple cities. There is secular Jerusalem, where I grew up. There is Orthodox Jewish Jerusalem, and then there is Palestinian Jerusalem. Obviously, it's not the same as in the story - we were not required to ignore the other cities. We just preferred to. There ostensibly was one authority above them all, but in practice, there were different laws and norms, different law and norm enforcement, and those travelled with you. It didn't matter if I was in the East or West, I would have been treated as a secular Jew. A Palestinian would have been treated the same in both too (not necessarily worse - this isn't Gaza I'm talking about. Just, different). The 2 cities in the book were alien to me as well, but they are not as far away from reality as you suppose.