As far as I am concerned, I believe that psychometric testing should be done by qualified personnel. Tests like these have to be assessed, and that can only be done by someone qualified to interpret the results and write a report.
Furthermore, these tests need to be designed for the specific requirements of the job. I, for one, would never submit to a test that some amateur found on the internet and decided to use without knowing how to use it and its relevance to the job. That is just stupidity.
I have undergone psychometric testing before, but I was sent to the office of a psychologist to do the tests and to have a psychological interview with her after she had scored the tests. Unfortunately, I never saw the results, and I would be very interested to know what she said about me!
The other thing to keep in mind is the relevance to the job. I cannot think of too many jobs where psychometric testing would be necessary. The job I was applying for was a high-security position in the Australian Government.