Some may find this statement a little hyperbolic, arguing that morphological stasis does indeed exist. But I would argue that the concept is much better abandoned; for two very simple reasons. One, that stasis in certain features does not mean stasis in everything, and the focus on what is unchanged causes people to totally miss all that has changed. Two, and linked to this, is that the concept leads people to fundamental misunderstandings of the fossil record and the history of life.
Describing something as a 'living fossil' is often simply a declaration of ignorance of the diversity of a group of organisms. Organism x is the only living representative of group y, and group y have been around for 200 million years! Therefore x is a living fossil.
One of the first Google results I got for living fossil, a list on the website Mother Nature Network, exemplifies this misunderstanding in its choice of living fossils; going so far as to include the platypus. The platypus is often described as primitive, but this is nonsense – it's not bizarre because it's primitive. It's bizarre because it's weird and extremely derived. MNN informs of 'platypus-like fossils' date back 167 million years; but this is falsely equating 'platypus' with 'monotreme'. The platypus fossil record is much more recent and only consists of teeth. We don't know when the various unique features of the platypus appeared; but there's no evidence they're especially old.
You may protest that this is a just a particular case of an amateur journalist's ignorance; but such misunderstandings are rife throughout descriptions of living fossils – even in the professional literature. Consider a classic case – the coelacanth.
Aside from the size (modern coelacanths are large compared to most, but not all, fossil species), modern coelacanths (that's Latimeria, at the bottom) have completely different fin configurations to most; presumably related to their bottom-dwelling lifestyle, and a very different skull shape. Latimeria's fin bones are almost symmetrical, unlike the configuration of even known fossil crossopterygian. Fossil coelacanths all have ossified swim bladders – Latimeria does not.
Coelacanths are not an example of morphological stasis. They're more similar to fossil coelacanth's than anything else alive because they are coelacanths; but they're not fossil coelacanths. They're a new, modern, derived form of an ancient and diverse group. Like pretty much everything else on earth.
I could write more, but this probably far too long for an OP already, so I'll leave you with this lovely collage from Darren Naish, showing artists impressions of various members of another group known, incorrectly, to have remained unchanged for many millions of years.