I sing the lake of pontchartrain.
yes, usage does determine correctness ,and if you went to louisana evryone would be referring to lake pontchartrain [singular].,and singing it as it was collected in loiusana in 1958,using the singular.
And with the greatest respect, the fact is there is, one lake of Pontchartrain,IT IS NOT IRRELEVANT,Christy Moore Popularised this song, as he did, Sweet thames flow softly[on this one he left out a verse ]in his SONG BOOK.
But because he uses the plural, but the population of loiusana ,does not, does not make him right,In fact VICE VERSA.,using the usage argument
that is why I say Christy Moore is not very good at being definitive[even though he is a fine singer]and his definiton and use of the word TRADITIONAL does not clarify what this word means, and does not help this discussion.