Excluding those that jumped the pond and were materially altered here tends to hide the rich song history in the New World. Take a hymn like Beulah Land and look at all of the variants the pioneer and regional singers created. They don't have "authors" at this point, but they are completely distinct from the original. Link to DT.

There are also "fake songs" that are popular but do have an author, such as the Pacific Northwest's Frozen Logger, written by an Oregon Newspaperman (James Stevens). Link to DT. Our history is shorter, all within the period of the written word in books and journals, it's easier to find the author of songs here.

SRS