a good deal of the tradition is formulaic and leads to the suspicion collectors did indeed pick songs that fitted their idea of what old music was

Collectors were mostly pretty explicit about that they were doing, and you're deliberately misrepresenting a completely logical set of priorities. If you're in a community where two sorts of stuff are being performed:

1. songs and tunes deriving from printed sources you're familiar with already and only adapted to a limited extent

2. stuff you've never heard before, which seems to be unknown outside this community, and which might be forgotten in the very near future as this community's way of life comes to an end

which is the more important one to record?

For sure, we now think it is ALSO important to record a complete picture of the community's musical practice, including what they do with materials imported from outside, but the collectors of the early 20th century got their priorities basically right about what to do with the limited time and resources they had.