Paddy and Patty are pronounced exactly the same in most varieties of American English, FWIW. If I had heard it said, I'd have no idea what it was spelled like, wouldn't care either.

Many people in America, I think, are wary of the term "Paddy," as they are familiar with it as a somewhat pejorative or coarse term for an Irish person. When I sing the couple chanties with "Paddy" in them, I can tell some of the American audience is not sure whether or not they are supposed to be enjoying it fully :) ... it's as if I sang a song with "Negro." They may be incorrect to think so, but that's the way it is.

"Patty" reminds me of Patrick, however incorrect that association may be. Patrick > Pat > Patty.

I am not disputing it being wrong. Just offering evidence to possibly explain the reason behind it (because we are talking about an event in USA).

Also, "paddy" makes me think of rice...and "patty" makes me think of peppermint patty, which has a cool refreshing flavor of mint...which is green... which is basically all St. Patrick's Day is for most people in USA: a bunch of green nonsense and drunk fools. It's Cinco de Mayo plus green stuff. In other words: I wouldn't take any displays of it in USA to heart!