Clearly you never watched the show.
Troi is not human. She is an alien empath. An empath is capable of reading emotions in humans and other aliens, although not actual thoughts. Her purpose on the ship was not just to be a psychologist for crew members but to ascertain the motives of new aliens they might encounter. The universal translator might convert speech, but she was there to identify when the words didn’t ring true compared to the emotions of he aliens speaking.
She was more the political officer reminiscent of the USSR’s ships.
So the entire command staff of the TNG was so emotionally fragile they had to drag an alien psychologist around so wouldn’t curl up into the fetal position at the sight of the first bug-eyed alien that said “BOO!”