I expect the amount of DNA we share would support this taxonomy. About as good as any. So to summarize, it’s the ability to have babies togeter that makes a species. I’d say your wolves and dogs example means there is some correction to do to the species taxonomy based on this rule though. Even wolves come in diffferent species: the dire wolf (Canis dirus), the gray wolf (Canis lupus) and the coyote (Canis latrans). One additional species, the domestic dog ...etc etc.
You are correct on the taxonomy for wolves and dogs being adjusted. DNA tests have shown that the wolf and dog are the same. My Chihuahua thinks she is a wolf and acts accordingly. The domesticated dog in all its different forms have the same ancestry. I suppose that if a certain type of dog became extinct, poodles for instance, they could be recreated over generations starting with a pair of wolves..............