Your assumption in the very first paragraph is that they are a good way to independently evaluate people's abilities.
It makes perfect sense to look for a way to evaluate people before we hire them. It's a real problem, and we must do something, but do we have any basis to say that the whiteboard interviews correlate with good performance. Otherwise, we go back to the classic "syllogism" to justify policy proposals
1. This is an important problem, and we must do something.
2. X is something.
3. Therefore, we must do this.
I've been developing professionally for over 15 years, and I am quite good at whiteboard interviews: 100% offer rate. That said, Many of the best developers I've worked with are not any good at whiteboard interviews, often because they lack the composure under pressure, or like to take some time to think everything through, which are correlated with scoring badly in those interviews. Therefore, no matter how good their code is, they'll have a lot of trouble getting into a company that does whiteboarding interviewing, or even practical interviews under time pressure.
I also have found that, in my list of things on what makes an effective member of a programming team, being able to come up with a DFS algorithm under pressure is nowhere near the top of the list. An attitude towards trying to learn what others bring to the table, instead of discounting them immediately because they aren't good at some specific CS shibboleth, is far closer to the top though. We just test for random algorithm questions for this because it's easy to measure, not because it's really all that helpful, and that's pretty unfortunate IMO.