I think it's not about diversity, but lineage. The phenotype for "fish" is so tight and well defined; a salmon is closer related to a human in the tree of life than to a coelacanth even though both are categorised as "fish".

I think you got that comparison backwards.

A coelacanth is a lobe-finned fish which is the group from which tetrapods, and thus humans, evolved.

A salmon is a ray-finned fish which is a very different group. These groups diverged sometime around 300MYA.