Well, first of all, the criticisms I can give of the genus-species distinction in biological taxonomy does not mean that the system "doesn't work." There are just pros and cons on this.
Pros of Genus-Species Distinction:
Organizational Tool: The genus-species distinction provides a standardized system for naming and classifying the vast diversity of life. It provides a universally accepted language for biologists to communicate about specific organisms.
Understanding Relationships: It helps in understanding the evolutionary relationships among different organisms, showing who is related to whom.
Research and Conservation: It aids in biological research, conservation efforts, and laws regulating wildlife, as species are the fundamental unit of conservation.
Cons of Genus-Species Distinction:
Lack of Clear Boundaries: In many cases, it's difficult to draw a clear line between one species or genus and another. Ring species and organisms with continuous variation across geographic ranges challenge the concept.
Struggles with Microorganisms: The system is less effective when dealing with microorganisms like bacteria and archaea, which can engage in horizontal gene transfer, blurring the lines between species.
Doesn't Reflect Evolutionary Fluidity: The static nature of the genus-species system does not accurately reflect the fluid, dynamic nature of species as shown by evolutionary biology.
Hybridization Issues: The existence of hybrids, viable offspring from two different species, challenges the concept of species based on reproductive isolation.
Genetic Variation: The advent of genetic sequencing has shown that there can be considerable genetic variation within a species, sometimes even more than between different species, questioning the validity of the genus-species distinction.
For a more in-depth discussion of these issues, you might want to look into evolutionary biology or philosophy of biology literature. A good starting point might be the works of Ernst Mayr, who was influential in the development of the "biological species concept", or the writings of philosophers of biology like Elliot Sober and Michael Ruse.
However, I repeat. despite all these criticisms, the genus-species distinction still provides a very useful framework. It is a fundamental tool in biological research that has proven to be highly effective for centuries.