There are problems with the current system, though. The one I'm most familiar with runs like this:
1. Species was named a while ago, with the type specimen kept. Name, say, Foozy yanner. Specimens are collected from several places over time.
2. Then we realize that those specimens represent more than one species (very possible just with old-fashioned naturalist observation, and happens also with genetic analysis).
3. So some of the specimens now are officially Foozy tanner -- but we aren't allowed to rename Foozy yanner itself (rules of system).
4. When you run across a reference to Foozy yanner it's _very_ difficult to know whether it's referring to the old unknowingly inclusive set of species, or the single (?) species that `Foozy yanner' now indicates. We'd be more precise if, e.g., we called the single species Foozy yanner_1, which might later get split to Foozy yanner_2 and Foozy tethera, with Foozy yanner_2 the name that includes the original Foozy yanner type specimen.
And this can happen with vertebrates! Archaea, hellifino.