What factor is critical in determining the locations where Xenacanthus fossils are discovered?

Its obligatory freshwater existence

The single most critical factor governing where fossils of Xenacanthus are located and recovered is its absolute requirement for an obligatory freshwater environment. This necessity immediately separates its fossil record from the much larger collection of Paleozoic shark fossils, which are predominantly marine. Finding a Xenacanthus specimen dictates that the sedimentary rock layer being studied must have once formed part of a non-saline body of water, such as a large lake or an extensive river system. This environmental constraint dictated both where the animal lived and, consequently, the specific types of geological processes—those that preserve inland riverbeds and lake deposits—that were necessary for its eventual fossilization millions of years later.