Nothing in the case required him to be evaluated - he’s made no comment on his own mental health or made it part of the trial - therefore it would be an invasion of his privacy. He did allow a previous therapist to be subpoenaed and he read his notes about Depp from the time. The therapist was not happy about it.
Depp’s behaviour was discussed as showing traits of a Narcissistic Personality - but Dr. Spiegel, who made the statement was forced to admit that he didn’t ever talk to Johnny Depp and it was speculation. That was one of the most interesting and colourful parts of the trial.
Amber Heard alleged she suffered from PTSD as a result of Depp and so there was a need for individual evaluations. She returned scores on the test that were seemingly comparable with battlefield civilians fleeing war zones, and they built a case around the fact she was likely exaggerating based on beliefs of what PTSD is like rather than truthfully answering the questions.