The opposite. Are you breaking the rule to leave your private stuff home just because the other side is or are you capable of keeping out of such sources of interpersonal conflicts, take over and redirect the discussion back to a professional level?

Of course it depends for what field and role you apply. For any leading role or customer contact point the capability to stay professional is essential. If you flip burgers at McDonald's then it's your right to be grumpy.

You are literally saying it’s a good idea to attempt to entrap potential employees by intentionally behaving the way you want them to not. It’s like pouring margaritas for you and the interviewee and then after they take a sip you say you don’t hire people who drink on the job.

This is unethical and it’s also a shitty filter because they people you want to hire (the ones why won’t talk personal stuff at work; or won’t drink on the job) are likely to write you off because they also don’t want to work with the guy who wants to drink margaritas and chat personal trauma at work.

I am literally saying that the role the person applied to was for a "founding engineer at a mental health startup".

This is a leading role(!) in the mental health(!!) industry. That should give some clues. They also announced that the follow-up interview as a "non traditional - a ~90 minute culture fit chat" dropping more hints.

Unfortunately he also "fail to recall the exact wording of the discussion topics".

I bet the exact wording was open enough to leave enough room to not "felt completely emotionally drained" afterwards.

I think the interviewer did him a favor. He is just not able to handle a leading role in the mental health industry in a way that would have been mental healthy for him.