"You'd be shocked how many people that write years of relevant programming experience and fail that."
Do you find people who did well on a preliminary test where they wrote some code fail this? If not, then why do the whiteboard? If people do fail, do you assume it's because they cheated on the previous test?
I think your stated explanation is incoherent, because you are claiming that self-taught developers can "get something done" without being able to write your ultra-simple algorithm. How can that be? You're not saying that someone can't handle B-Trees and you therefore won't hire them, you're saying they can't do anything and yet somehow they were hired and do stuff at other places. If they can "get something done", why are they useless?
If your comments are based on a lot of genuine experience and sincere and heartfelt, had you considered that maybe what's going on is simply that a large percentage of the people in the industry do not and cannot do whiteboard programming, but only write code at a computer? I have literally never had to, to get a job, and I'm not sure I can remember doing it in undergraduate classes either.
Joel Spolsky (and no doubt others) wrote something about how you can't hire the best people by just advertising a job because mostly the same people apply to all the jobs and the really good ones aren't in your pool.
But a corollary to that, I think, is that when you do hire some decent people, and you go on doing it, because it worked adequately, you are likely to wrongly conclude that is what decent people look like. It's not just the rock stars that are missing from your pool, it's the people who are terrible at interviews and are much more loyal to a job than those who can handle whiteboards and small talk. You may be in a bubble where you, and the people you hire, are working much harder than people in another bubble, but it's just a different way of doing things, not the only way.
I think this idea of your hiring pool not being representative and getting wrong ideas of what good and bad people are like has implications for diversity of various types, but I'm not going to flesh that out here.