I do think SNW tends to overuse established characters, and I see no reason for the transporter chief to be Kyle. But in general terms of new adaptations of old works, the answer is that the characters in those works are overwhelmingly white, which is unrealistic in this day and age and often would have been at the time (for instance, the Old West had far more people of color in it than you'll see in most Westerns). So it makes no sense for a modern production to perpetuate that unrealistic bias.
Also, saying "people of color shouldn't be allowed to play legacy characters" is just one more way of perpetuating white privilege, of saying that a monopoly rooted in racism should be preserved rather than torn down. Ideally, every role should be open to the best actor for it. They're all imaginary, after all. Characters have no absolute reality, so it's easy to change them to fit actors. There have been productions of Shakespeare where noted actresses have played King Lear or Prospero. To insist that an imaginary creation must be immutable is misunderstanding the nature, and the power, of creativity.
Gene Roddenberry apparently approached Star Trek as a dramatization of Kirk's logs rather than a literal depiction, and thus was perfectly fine with making changes to correct earlier shortcomings. When he had the Klingons redesigned for TMP, he asked fans to accept that they'd always looked that way and TOS had simply gotten it wrong due to limits of budget and technology. So I'm sure he'd be just as fine with saying that, say, Robert April was always black and "The Counter-Clock Incident" just drew him wrong.