I'm not saying that the Byzantine text is correct 100% of the time, and in fact, the KJV uses a somewhat strange version of the Byzantine text, but I believe there's still a better case for it as a valid source than there is the Alexandrian version, whose greater manuscript antiquity can be attributed to entirely to climate.

If you get a version of Pierpoing and Robinson's Greek New Testament, there's usually a very readable essay explaining exactly why, from a historical perspective, it's more likely that the version preserved by the Church has less error.