The union of thought and emotion doesn't mean the lack of individual thought.
If the lack of individuality was true, the Dark Templars would have not existed because they would have been unable to considering the act of separating.
It seems like you are mistaking a telepathic link between everyone to equate everyone are robots. The Protoss aren't robots, but at the same time, they have a collective bond, while still remaining persons and individuals.
In-game explanation: When Artanis tasked Karax with investigating the key, he complained that he was unable to share thoughts with the other phase smiths, and it is difficult to work alone. The fact that he "feels alone" and not "sit there drooling" means they have individual thoughts, even when connected via the Khala. The Khala seems to allow instantaneous sharing of thoughts and ideas.