Is Hakai a technique impossible for Goku to master?
No, for now. Hakai is a technique that can only be achieved by a god of destruction. If ur not a god it is impossible to master the hakai technique. But thats only looking from the anime. In the manga goku is able to learn hakai in a fight against fused zamasu. Sadly in the manga debut toriyama hasnt comfirmed for goku learning hakai to be canon.