The environment I describe is not universal, nor did I claim it was. In fact, I am advocating walking away from the subset of companies that do whiteboard interviews.
About your reply for point #1, I agree that communication and collaboration are important. I have picked up chalk (I'm old) during an interview in order to draw diagrams related to robot paths. But you'll note that I decided that the chalk-talk was an effective way to communicate essentially visual information. A "whiteboard" interview is one where the interviewer decides that I need to use a whiteboard to communicate. Coding is not a whiteboard activity and the medium choice is inappropriate. I rarely choose to communicate algorithms with an interpretive dance for that very reason.
About your reply to point #3, in any large company it is highly unlikely that a single, new-hire person would have such a broad scope of activity. Hiring a person of that scope would cause me to invest in background checks and presentations by the person showing their prior projects, designs, and outcomes. I certainly would learn nothing by asking them to reverse a tree on a whiteboard in 20 minutes.
As to your final point, I did present a superior alternative. Have the hiring manager talk to the person about the job opening and the skills expected. Ask the person to provide related background information from their prior experience. Ask them about how they might appoach a current or previous problem related to the job opening. If THEY want to use the chalkboard to communicate that's fine.
An interview tells you a lot about a company and how it treats employees. If you see a "sea of desks" in a supermarket-sized open-plan floor you can assume you're "just another ball in the ball-pit". If they hold meetings in a fisherman's net strung from the ceiling (I wish I made that up, but no...) then you can assume they have a playground mentality. If they are proud of their "80 hour weeks" you can assume your pay rate is only half what it claims. If "free food" is given as the best reason to work there, you can assume the work is painful and boring. And, to the original point, if the interview process resembles a frat-house hazing-style "paddle line" of unrelated interviews, you can assume a frat-house "good culture fit" mentality. Every frat house strives for a monoculture (as in, "we only hire the best and the brightest").
But if you're a professional, working every day to improve your skills and breadth of knowledge and experience, then respect yourself. Walk away.