In their overturning of the Textus Receptus, Westcott and Hort had no access to early papyri discovered these last 100 years or so. If they had, then they would have said, "And what's more, the Byzantine Text Type is not represented in the papyri."
The discovery of the papyri also had a counterbalancing effect, though. Westcott and Hort thought that Codex Vaticanus represented the pure form of the Greek New Testament. To be sure, Codex Vaticanus almost certainly represents the purest manuscript available to us, but it is only "relatively pure."
Some people on the Byzantine Priority side of the debate have gotten hold of some of this latter argument, and have claimed that certain readings which conform to the Byzantine Text Type give evidence that the Byzantine Text Type was early. This is a misrepresentation of the evidence. Yes, some individual Byzantine readings are early, but a Byzantine text type or text cluster is not represented in the papyri.
Eldon J. Epp divvies up the papyri according to four groups: A (Byzantine, with Codex Alexandrinus its early representative); B (Alexandrian, with Vaticanus its leading representative); C (P45, W, and other mixed manuscripts somewhat mixed between the Alexandrian and Western text types, formerly conceived of as the Caesarean text type); D (Western Text, with Codex Bezae its leading representative.
The following chart, which shows which papyri belong to which group) reveals how wrong the Byzantine prioritists misuse the data:
A (Byzantine): none prior to the sixth century
B (Alexandrian): 37 prior to sixth century
C (Western-Alexandrian mixed): 5 candidates prior to sixth century
D (Western): 11 prior to sixth century
["The Significance of the Papyri for Determining the Nature of the New Testament Text in the Second Century" in Studies in the Theory and Method of New Testament Textual Criticism by Epp and Gordon D. Fee; the article was written in 1988, and more early papyri have since been found, none of which can be classified as Byzantine.]
The point is that the Byzantine Text Type is not represented in the now over 125 papyri presently extant.
One thing is absolutely certain: the papyri do nothing to help the Byzantine Text Type advocates and the KJV-only/TR advocates. They only disallow the rejection of individual Byzantine readings solely because they're Byzantine.