Give to any musician, and they'll play it that way.
Ive never thought of this before, but I think you are correct.
Ive just checked with an instrumentalist. Ben Webster.
Its said that he couldnt/would play a song unless he knew the words.
https://www.youtube.com/watch?v=ZVqgct8LEdw. ( 1.15 )
Even allowing for the twiddly bits, he is still playing it your way.
His way makes the most musical sense to me.
I think its just gershwins attempt to squeeze a rhyme in even when it doesnt make sense that causes problems for singers, in respect of them trying to make sense of it from a language point of view, as well as a musical.
Maybe I need to learn some more lyrics..