I doubt if the sipngs Burns collected were sokld in enourmous numbers - his own poetry was but Johnson's 'Musical Museum' was somewhat confined in its sales, I would have thought - immaterial anyway

I deal with one consequence of that every week - pricing early editions of his works (which always included the songs he collected along with the original stuff). By the time you get to the 1812 editions they're not worth beans.

There is any amount of corroboration that he was a household word all over Britain, Ireland and North America long before the end of the French war. Allusions to his life and work in letters and newspaper articles never needed footnotes. To a lesser extent you could say the same about Tannahill, Campbell, Moore, Dibdin - singable folk-ish poetry got everywhere.