"To me it's interesting only because if collectors can have only come up with a vanishingly small number of tunes in Lydian or Phrygian or anything else, it means that, at least over the past 125 years or so, there has simply been no significant use of those modes in tradition. Why not?"
Maybe it's significant that Lydian is the most major and Phrygian is the most minor of the modes, would there be a tendency for the Lydian to migrate towards the Ionian(modern day Major) and the Phrygian towards the Aeolian(modern day Minor).
That is, the Lydian dropping the augmented fourth(Bronson h1) and the Phrygian dropping the minor second(Bronson h5).
From what I remember Bronson found that around 3/4 of all appalachian ballads are hexatonic or pentatonic. So even if they originated in strict modal form(???), they may have been gapped to accommodate local forms of harmony singing.