"New York, New York" - Big Mistake!

In the song made popular by Frank Sinatra, "New York, New York", there is a glaring mistake in the beginning of the 3rd verse:
"I want to wake up in that city
That doesn't sleep ..."
By waking up, presupposes that you've been sleeping, which contradicts the city "that doesn't sleep".
Come on song-writers! You can do better than this. How about,
"I want to wake up in that city
With a big-titted bitch-whore" ?
New York, New York Frank Sinatra

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