Some of the claims here feel like leaps of intuition. You claim companies don't but many companies, especially ones that are not in the tech industry, do employ personality quizzes in their screening process. Even tech companies, now that I think about it, employ a personality test in the form of a "cultural" interview. I am dubious on how helpful they are but they highlight the real issue which is that there simply isn't enough signal during the interview process.

Every hiring process boils down to a risk mitigation problem and the goal is to get enough positive (or negative) signal to make a hiring decision. If that's the case, making the interview an "adversarial" process seems like an awful idea. As you pointed out, why would a candidate share information that puts them in a bad light? It creates an environment where it is hard to extract meaningful signal.

Furthermore, if there's no free lunch from analyzing personality, then why is it worth thinking about in this way? Perhaps it is more critical and effective to verify their skills and experience with the limited interview time and rely on references to validate their work habits.