Your comment is somewhat emotionally charged, but I choose to respond to the overall point as a mathematician. I think it could be true that utility is correlated with difficulty but it is certainly not defined by it.

In pure mathematics, we reason about a world of abstract objects which are considered interesting ab initio. It may be because they arise directly or often from extremely basic operations, they are connected to many other interesting objects, or that they present special and surprising properties. The importance is basically, there is some surprising, interesting, phenomena which occurs in our world which we don't understand and which we seek to understand. Like science but in the non-physical world.

I think if you create a simple to describe system/construction with a property which is extremely difficult to prove. You are creating an object in our world which is basic but have properties which we don't understand (because we can't prove this property). So indeed I believe it would be an interesting thing to study and be of value. I don't see any problems/issues with this. I don't think the only valuable pursuit of humans is to improve the welfare of other humans. I think understanding the world is also valuable.