Don't know but speculation: classical ragtime as exemplified by Scott Joplin, James Scott, Kerry Mills ETC. often featured two parts and a "trio" which was a third part, usually in the key with one less sharp (a fourth higher). And now that I think of it, the Sousa marches that I played in HS band a long time ago would do the same thing. So. . . "composers" of polkas followed an established pattern. (Next question-- why that pattern? dunno)