An assumption is being made here that Child had access to all 'ballads in his time frame.

Apparently no one reads his "Advertisement to Part I, Numbers 1-28, written in December 1882." His 'Advertisements,' or introductions to the parts, contain information on the problems he had in assembling this mighty collection. No one since had done anything of this magnitude.

Quoting Child: "It was my wish not to begin to print 'The English and...'" until this unrestricted title should be justified by my having at my command every valuable copy of every known ballad. A continuous effort...some eight or nine years...and many have joined in it. By correspondence, and by all-extensive diffusion of printed circulars...tried to stimulate collection from tradition in Scotland, Canada and the United States, and no becoming means has been left unemployed to obtain unsunned treasures locked up in writing."
He goes on to speak of lost treasures, such as the Percy Manuscript, his inability to obtain access to several manuscript collections, etc.
He speaks of and thanks the many contributors who loaned manuscripts.

Like any compiler, he was limited by what was obtainable. Also remember that additional materials have become available in the over 100 years since he published.