My sister, a pediatric ER nurse would disagree with you. The interviews are largely behavioral and are a breeze. No dummy is wheeled in with head trauma, random "new" diseases aren't invented and asked to be treated, etc. The simple fact of the matter is if hospitals hired in the same way, they would have no staff.
I know it's totally anecdotal, but we've all heard horror stories about candidates who couldn't write a for loop; some of us have witnessed these things first hand. And yes, phone screens should be filtering out those sorts of candidates long before they start sweating with a dry-erase marker in their hand, but, well.
How likely is an applicant for a nursing job to flat out not know how to stitch up a wound, or to take a patient's pulse and temperature?
I have no idea what the candidate did in their CS undergrad. Maybe they cribbed all their work from their roommate. Maybe they went to a party school. Maybe they spent the last 4 years as a 'Senior Developer' at FooCorp copying files from hard drives to floppy disks, and posting a few paragraphs a day on the company's WordPress install. Maybe they are an Architecture Astronaut who can talk for six hours about how great Haskell is at doing multi-manifold monadic trivariable entaglement, but has no idea how to do any real work.
Or maybe they spent the last decade building Bigtable and MapReduce, and Spanner, and TensorFlow at Google. I'm not an expert on Bigtable, or MapReduce, or Spanner, or TensorFlow, though - and I can't definitively, in 60 minutes, tell if the person I'm talking to is bullshitting me. I can't tell if they actually did any of that work, or they coasted. I can't tell if the complicated problem they are describing to me is actually hard, or if they are embellishing it. Even if I felt confident that I could make that conclusion, my opinion would be incredibly colored by personal biases.
Oh, I should check their GitHub, you say? Well, guess what - Jeff Dean - the guy who did spend the last decade building Bigtable and Mapreduce, and Spanner, and TensorFlow - doesn't have a GitHub account. Presumably because he has better things to do with his free time, then work on OSS.
Oh, I should hire fast and fire fast? Don't get me started on why that doesn't work...
Once you're an RN or an MD with all the appropriate qualifications, assuming you're not outright faking them, they can be reasonably confident that you are, in fact, a competent nurse or physician and move on from there.
We don't have that, and so we have to spend a lot of time making sure that a prospective candidate even has the basic skills and qualifications of a software engineer.
I had to do that at my last interview. I got through it ok-ish. The more interesting question was a more general system design question - how would I architect a system to do X, under constraints Y and Z. What would I do if a new constraint came up? Ok, now how would I make it more resilient? There, the whiteboards is just a tool I can use, not the primary focus.
But it's the interview equivalent of your driving instructor making sure you adjust your side and rear view mirrors before you start the car.
Honestly, we all might as well read chicken entrails because that would be about as predictive as our current interview practices.
I'm not opposed to white-boarding, but to reinforce this point I'll note that I would have done much better on some of these problems when I was just out of college than I would today, because they were all fresh in my mind.
I assure you I wasn't a better programmer or employee then.