In the early songs of the Beatles, one hears melodies that would seem to be more (a product of rural southern America than that of an English industrial city.)
Correct: a product of rural southern America than of an English industrial city.
Why is the original incorrect? Doesn’t the comparison starts immediately after “more”? So if you have “a product” right after “more” on one side, you must have “a product” on the other. Thus, A PRODUCT of a place is compared to A PRODUCT of another place?
The comparison does start after “more,” but there are elements of a comparison that don’t need to be repeated if they wouldn’t change. We don’t need to say “a product” twice, nor do we need to use something (“that”) in place of it.