Here's Ella singing...
Ella Fitzgerald: I Got RhythmHere are the lyrics...
Notice that in Section B, the section that is the memorable and defining section of the song, there are no rhymes. The only 'nearly a rhyme' comes from repeating line 4 as line 8.
It's also worth noting the following...
1. Ira used a very heavily rhymed section to lead into a non-rhyming section. This is guaranteed to make the non-rhyming section stand out.
2. The first 6 lines of Section A have a very sophisticated 3-line rhyme scheme that pulls lines 1 and 2 together by rhyming both(!) in the third line. How cool is that!
3. Section C with its XAAB rhyme scheme is left hanging unclosed from a rhyming perspective. This drives this section headlong back into the repeat of Section B.
4. The lyric comes to a close when the unrhymed and hanging word "door" in Section C meets its aural complement "more" at the end of the repeated Section B. This produces a satisfying sense of completion.
Summarising... after very heavily rhyming the introductory Section A, Ira is minimalistic with his use of rhyme for the rest of the lyrics. He also does not have any rhymes in the lyrics of the song's signature section (Section B) except for the final line of lyrics rhyming with the final line of Section C. At no time do any Section B lines rhyme with other Section B lines.
"Why do these lyrics of Gershwin's work? How has Gershwin added musicality to words without using rhymes?" are very eye-opening questions to think about!