First, I agree that we don't have voluntary control over what our intuition tells us.
Second, I agree that there is rarely a circumstance where we can actually prove our intuition is correct. But in most cases, I would say that our intuition delivers ideas to us that are close enough to being correct that those ideas help us get along in the world.
Third, I think that the cases in which intuition can be proved incorrect are outside the normal judgements ordinary people must make in order to successfully run their lives.
Fourth, I agree that "almost everyone wants the world explained to them in a manner such that their intuition will give them the correct answer."
"Now doesn't that strike you as a rather stupid and short sighted theme to use in trying to understand the world"
Not if you are simply trying to understand the world at the level at which you must interact with it in ordinary living. If you are trying to understand the world at a deeper level as a scientist, then, yes, intuition alone wouldn't be sufficient. Then again, science doesn't limit itself to intuition in arriving at theories.
"It seems to me that any rational person would recognize that, in view of the facts listed above, they want something which most probably can not possibly be achieved. "
I don't think people in general want, need, or expect proof. All they need and want is a belief that is sufficient for their survival. If the world works pretty nearly the way they believe it does, they can get along without too much risk. They don't need to know the truth.
"Why do they waste their time in such a fruitless search? Is it perhaps that they just prefer not to think?"
Most people don't waste too much time on such a search. Many of us who do waste a lot of time on it simply do it for the fun of it. Maybe I'm misunderstanding what you mean by "fruitless search", but I think it takes more thinking to engage in such a search than it does to simply act on the intuitions we have.