As a palaeontologist the taxonomy and systematic work I do (and of course analyses built of these) is based around the morphological species concept. There are lots of species concepts out there (over a dozen as I recall) and these are there to take into account the vagaries of evolution and biology. Most people will be familiar with the idea that a species is a group of organisms that cannot successfully reproduce with another. This reproductive species concept is fine as things go, but it can’t work all the time. What about asexual lizards or bacteria? What about animals that can interbreed but don’t because they are separated by a barrier like a river? And testing this is not always feasible – should we be trying to interbreed all manner of seals just to make sure they are species? And of course, what exactly do you do with fossils?
And so enter the morphological species concept (or hereafter MSP to save me typing it out all the time). With no possible way of looking at interbreeding, genetics, geographical isolation or other issues with fossils we must work with what we have and that is the anatomy of the animal to hand. Thus the MSP uses differences in the anatomy of specimens for taxonomists to judge their membership of species.
This is not as daft as it may first sound. After all, most species can be separated in multiple ways – they have different genes, breed with only their own species, live in different places, behave differently and so on, but they also look different. Based on living animals the average person will be struck by the different colours or patterns of different species or major differences in size, but dig deeper and their skeletal anatomy will be different too. Different antelope species have different horns, different cats have bigger or smaller canines, lizards have very varying tail lengths and so on.
These are of course simple and dramatic examples, but it should be intuitively clear that species can be separated out by their anatomy and that using this as a basic for defining them (and indeed other taxa of higher ranks) is a perfectly acceptable way of doing it. Of course this still requires caution with intraspecific variation and the rest, but the MSC as an idea is perfectly workable and no more imperfect than any other. It does also have the benefit of being relatively easy to cross compare with all manner of species both living and dead, which isn’t true of many others.