Psych tests are not designed to only eliminate psychopaths. I would suggest your perception of these HR departments is narrow and somewhat ignorant. Psych tests are one of the most effective ways of drawing a picture of a candidate's persona, motivation and work ethic. The airline can then establish a certain culture from day one by picking the personalities they want (to a certain degree, obviously). No system is perfect, the pysch tests are pretty damn effective though.
It takes VERY little effort and research to debunk and fool even the most involved Psych test.
It is far far more effective to have a trained interviewer, who is able through a combination of technique and experience to extract (yes extract) the key motivations and attitudes from a candidate.
In many cases airline HR departments are a self perpetuating philosophy, on the one hand justifying their existance by filtering "unsuitable" candiates, and on the other hand making increasing demands on those who apply for positions by employing ever more eloborate and pointless exercises which only "prove" how many "unsuitable" candidates actually exist out there