Welcome to LessWrong. There's a sizable contingent of people in this community who don't think that uncomfortable truths need be confronted. But I think they are wrong.

As you say, one purpose of believing true things is to be better at achieving goals. To exaggerate slightly, if you believe "Things in motion tend to come to a stop," then you will never achieve the goal of building a rocket to visit other planets. You might respond that none of your actual goals are prevented by your false beliefs. But you can't know that in advance unless you know which of your beliefs are false. That's not belief, that's believing that you have a belief.. And adjusting your goals so that they never are frustrated by false beliefs is just a long-winded way of saying Not Achieving Your Original Goals.

In theory, there might be a time when you wouldn't choose differently with a true belief that with a false belief. I certainly don't endorse telling an imminently dying man that his beloved wife cheated on him years ago. But circumstances must be quite strange for you to be confident that your choices won't change based on your beliefs. You, the person doing the believing, don't know when you are in situations like that because - by hypothesis - you have an unknown false belief that prevents you from understanding what is going on.