I think the word "even" in the title of the thread is interesting. It seems to imply there is a close correlation between things that are "useful" and things that are "true", such that deviations from this rule would be exceptional rather than commonplace. But is that really true? I'm not sure that's an assumption that should be granted in the fire place.
Which actually touches upon one of the most compelling arguments in favour of God: the argument from evolution. Because if we grant evolution as true then out mental capacities are a result of a long process of refining cognition in the direction of what is useful for survival. And what is useful for survival is not necessarily what is true about the world.
One example (probably not the best since it is disputed) is the psychological bias toward optimism that most humans share, except those who suffer from depression. It's a consistent finding of psychologists that humans are extremely poor at judging risk, and for example consistently underestimate the chances of them encountering major difficulties in life such as major illness, bereavement, unemployment, separation, injury, crime and so on. Interestingly clinically depressed people are much better at assessing the true odds of encountering negative life changing events. Yet the price they pay for having this "true" picture of reality is a mental condition which can be extremely debilitating. The point being this is an example where a "true" picture of reality is not "useful" in that it impacts a person in ways we would normally judge to be detrimental.
In a broader sense, if evolution is true, then it follows that our mental perception is a tool which has been shaped for survival rather than a tool for accurately depicting the world around us.
