There are many co-existing species concepts used in practice that are statistically rigorously defined, selected according to the biology of the lineage in question (e.g. it makes little sense to apply the same concept to both recombining and asexual lineages). It's an intensively researched area that becomes more refined and more explanatory with time, like any other area of science.

Delving into the recent literature might enable you to make a less clumsy critique. Independently evolving units of biological diversity exist. Any accurate knowledge about them, and about all the edge cases and fuzzinesses and genetic phenomena that make systematization complicated, comes from biology itself.