Except that some of the ultra-rich have major personality disorders which cause severe cognitive distortions and erratic and impulsive behaviour. Their power and influence tends to allow their cognitive distortions to spread in to the general population, which eases the cognitive dissonance that would be a problem for normal people. But anyway, these people cannot be compelled in to psychiatric treatment, and who could convince them? Who do they listen to? We're talking about a category of people who are notoriously difficult to get to enter treatment, even when they are not princes and emperors, but average Joes.
I mean, if a street sweeper thinks he is King, you might convince or compel him to get treated when he comes in to contact with the system. But when the King thinks he is King... that is a much more difficult problem to deal with.. usually the kingdom joins in with his madness so as to keep him happy.