"Orthogonality" of chemical elements
Certainly nuclear fusion and nuclear fission can convert elements into other elements. Indeed, this is how different elements form in the first place.

The one issue I have is with your "arbitrary chemical element." You can use fusion to put together lighter nuclei or elements into heavier ones - up to iron, or use fission to divide more massive nuclei into lighter ones.. up to about iron.

The limit here is the binding energy of the nucleus which maximizes with $\ce{^{56}Fe}$.

In general, though, your point is a good one. Given enough energy (e.g., in a supernova), you can create lots of different elements.