Steve Gardham asked

"Under what criteria should Child have included it?

"It is narrative and it has a long pedigree in somewhat different forms, but so have thousands of other songs."

Child himself never declared definite criteria, possibly changing his mind over the years, and certainly admitting that some of the ballads that he DID include had a very poor claim.

I presume that the thousands that you have in mind are the outpourings of the broadside presses, which Child evidently didn't think much of. But there are surely not that many narrative songs that go back as far as The Frog and the Mouse AND have remained current for so long. Unless he was totally unaware of it, which seems unlikely, there must have been something about it that made him reject it, but it's not obvious what that might have been. Perhaps the anthropomorphising? Some of the ballads that he did include have animals that talk, but not that behave like humans.