There's a wonderful quote being discussed at the Garden of Forking Paths. In my dissertation, I have occasion to discuss the connection between pragmatics and truth, and I discuss one prominent example of a disconnect between the two. Psychologically healthy people have an exaggerated sense of the amount of control they have over the world. They believe themselves to be able to influence random events, and to be able to exert considerably more influence over non-random events than they actually can. The tendency to over-estimate one's degree of control declines or vanishes in the case of the severely clinically depressed (even the severely clinically depressed do not tend to under-estimate their degree of control; on average the severely clinically depressed are fairly accurate).
In my dissertation, I note this widespread delusion of control as an example of a false belief that seems to be beneficial; obviously the severely clinically depressed do a poorer job of coping with the world, despite understanding it better. I also add in a footnote the point that's relevant here, namely that this illusion of power seems like it might account for the persistent belief in implausibly strong free will doctrines.