Two issues here. First, can genetics replace morphology for deciding whether two populations are one species or two? Answer: Sometimes. After all, different species no longer interbreed; they no longer exchange genes. Genetic analyses may be able to determine whether that’s true or not. However, there is no amount of genetic differentiation that indicates two populations are one species vs. two. Sometimes, a small genetic difference makes two populations unable to interbreed to produce fertile offspring. Other times, one species is highly genetically variable.
Sometimes genetic incompatibility results from translocations (rearrangements of gene order on chromosomes) or polyploidy (variation in number of copies of each chromosome). These can cause virtually instantaneous speciation, with, at first, no or few detectable difference in DNA sequences. And sometimes even polyploidy doesn’t prevent (though it does reduce) gene flow between, for example, diploids and tetraploids.
Sometimes there is clearly small morphological and genetic differentiation between two populations and it clearly results from geographic separation. Are the two populations one species or two? Would the organisms interbreed if they met one another? That’s a judgement call, and it can not be resolved with more data, morphological or genetic. Also a judgement call: where do we draw the line between asexual species? How do we handle populations that seem to be in the process of becoming two species but haven’t completed that?
Genetic analysis provides data for deciding what are species. Important data. But not a simple replacement for looking at morphology, behavior, etc.