I also agree with the core idea, but not several of the particulars. No, you can’t compile and test your whiteboard code, and that is in fact exactly the point. You’re not expected to write syntactically perfect code, just some pseudocode or boxes and arrows or some combination of both. It’s an impromptu oral presentation of your algorithmic thinking skills. If you can manage it completely with words, then so much the better: most of us still need to draw visual aids.
The problem is when one judges the quality of code designed on the spot using such a slapdash medium, and not the communication skills and forensic thinking that should be the abilities under test. Which is really a proxy for the bigger problem, the one I think we agree on, that whiteboard tests are more a Rorschach test, revealing more about the interviewer’s biased interpretations of squiggles and shorthand on a board than measuring anything objectively. Sort of ironic for a test ostensibly about communication skills.
All that said, I still expect one to know how to at least write a loop in some kind of pseudocode. Or if it’s a DB job, to throw together some basic E/R boxes and lines.