You're looking for the wrong things, and using the wrong terms of reference. There is no question here of "missionaries" "stamping out" anybody's traditional song culture; that culture was oral and unrecorded in the first place; from the point of view of a literate person, there was nothing to suppress. The fact that monks (as a rule, the first literate people in Europe) failed to record it is completely irrelevant. Why would they bother, even if they were aware of its existence? I'd suggest you read up a bit on medieval history before getting too involved in uninformed theories.