My feeling now is that the fact that it is arbitrary and doesn't have that much to do with real-life work may be a feature. You can dissect job performance in a number of ways but I think most people would agree that these four factors are important: general cognitive ability, conscientiousness, domain knowledge and motivation. And of those, domain knowledge is already relatively easy to discern from the resume and otherwise easy to screen for and if your company is doing anything unique, not as important in the long run. Almost any process would do a sufficiently good enough job of taking into account relevant domain knowledge. Thus what makes one process better than others has more to do with extracting other signals.
Whiteboard coding interviews, by being timed, somewhat arbitrary, yet something that is widely practiced and easy to study for, implicitly selects for cognitive ability, motivation and conscientiousness. It's hard enough that you can't be dumb, it requires enough preparation that you have to be somewhat motivated. And the process of preparing for interviews is sufficiently repulsive and it's easy enough to fool yourself that you're prepared enough when you really aren't, that studying to the point where you're prepared is a test of conscientiousness. This creates a paradoxical situation where the test itself isn't necessarily that relevant for the job, yet those who get through the test are almost always very good.
In short, given that what you need to do to pass these interviews is fairly widely publicized, the ability and willingness to do what it takes to pass positively signal that you'd make a good employee.
Even if you're great at software development, if you're neither sufficiently motivated nor conscientious enough to prepare yourself to pass these interviews, it's unclear to me why you'd also go out of your way to excel at any given job - every job requires you to do things you don't want to do, learn what you don't care to learn and deal with a variety of suboptimal situations constructively. So while I'm sympathetic to the point of view that this shouldn't be how things are done, I think the willingness to say, "you know, this is how things are, so let's deal with reality as it is instead of wishing it away and ignoring some of the best job opportunities because I don't want to study" is a positive characteristic. Every job has challenges like that - something that in an ideal world is kind of stupid, is not at all fun to do and takes a lot of effort, but doing it is strictly better than not doing it. You want to hire people who are willing to do these things, not just complain about how stupid it is.