So far, nothing new. That sort of setting is almost standard, although it was a trifle newer fifty years ago.
Here's the problem.
The author did a fine job of describing this enormous, enclosed city, vast almost beyond imagination, layer upon layer of moving walkways, ramps, corridors - you get the idea. Huge. Enormous. Far beyond anything of our period.
More accurately, beyond anything of the period in which the author wrote.
That wonderful description of a vast city-world would work fairly well today, except for a couple of details.
The author described where it was, and told the reader how many people lived in it.
In terms of geographical extent, his super-city was almost exactly where the built-up area on the east coast is - with Washington, D.C. in the south, and New York City in the north.
And the population of American's coastal 'megalopolis' is, if memory serves, roughly the same as that of the author's super-city. Just one difference. The author very clearly indicated that his super-city was crowded with people. Really, really crowded.
Now, I understand that there's continuous urban development between Washington, D.C. and New York City: But it's not all as densely built up as the south end of Manhattan Island. And the last I checked, Jenny Craig was still making money with a weight-loss plan. Starving, Americans aren't.
And the Lesson is: Check Your NumbersThe author, who should have known better on several points, failed to do some basic math. In written science fiction, I like to think that the author did a little checking: and if there's a city of a given area, with a given population, and limited vertical development: that the 'overcrowding' or lack of same will add up.
Today's east coast megalopolis is more built up than central Minnesota, where I live: but it's not a vast enclosed labyrinth, level upon level of swarming humanity, either.
I still like the story, but now I have to work harder to get that willing suspension of disbelief.