A person with some fixed 'value' X can be worth much higher to one company than some other company. In fact that is extremely common. Value is relative here so I completely disagree with your "a professional knows their value" sentiment.
If you disagree with "a professional knows their value," what are you arguing? That "a professional doesn't know their value?"
But I still think that refusing to name a number shouldn't be the number one point in all of these discussions and blog posts about salary negotiation. You're right, when there are huge amounts of information disparity, either because a company's pain point is significantly higher than market rates would imply, or because a candidate has a rare and unique skill that cannot be easily found, then all of the entry-level negotiating tactics go out the window. But for fair-market jobs and candidates, I think you should be able to know your value well and refusing to name a number is a waste of time and energy.
Well, in the podcast, he mentions that this one action is part of a larger strategy. The goal of it isn't to get the company to reveal the cap, but to defer the question until you've demonstrated high value to them, see where they start, and try to find their cap from there.
A professional might know their value abstractly or concretely to some companies, but in general value is relative to the company's needs, funding, and priorities. The recruiter has too many data points that you don't have to argue that going in with a fixed number is wise.
And even if you can do all that, there's no reason why the dollar value you put on your worth to them has to be similar to the dollar value they have in mind. You could argue, in that situation, that you may not want to work for a company that doesn't value you "properly", but I hesitate to believe that there's always (or even often) an objective version of "properly" that disinterested observers could agree on.
Having said all that, I am still not sure I buy into the idea that the best negotiation tactic is to evade (even "professionally") providing a number.