With that phrase, you may have suggested the answer to the "no new phyla" problem (or perhaps it should be called an observation rather than a problem). If all species are related by common descent, we should expect to see a gradual branching from common ancestors. And we do see this. It forms the tree of life. But you are objecting (if that's the word) that there is no new trunk forming, or at least no new major branch being developed.
In the Cambrian period, living creatures were quite small. I suppose the array of what existed may be analogous to life at the bottom of the oceans today. New forms actually may pop up from time to time. The variety of tiny creatures is amazing, and no one has catalogued them all. Some may be relatively new.
In any event, it's difficult to see how a new body form, if such shows up, is going to start developing enough descendants of various types to get recognized as a whole new phylum. The precursors would probably get gobbled up before the process developed very far. The existing "tree of life" may be hogging the show. So be glad our ancestors appeared when they did.
At any rate, according to the NASA guy, a sweeping hormonal change in a population could cause an entire new body plan in sufficient numbers to emerge and survive.
If it happened back then, then what would prevent a sweeping hormonal change in the population of humans which would cause enough with 3 eyes, 4 arms and antenna to emerge and survive?
People today would not call "that" a new body plan per se but they might if it happened to worms. Nevertheless, I believe it makes the point that something must be preventing sweeping changes to regulatory control genes after the Cambrian. And because of the eyes developing concurrently in both vertebrates and invertebrates, I suggest it is the control genes themselves resisting change.
As the Glenn Morton Phylum-Level Evolution page points out, one group of sponges has indeed evolved a completely different body plan from the rest of its group, or from any other living thing.
Vacelet and Boury-Esnault (1995, p. 335) relate:We don't actually assign a phylum to every unique body plan if we can see clear relationships by other means.
“Our results raise fundamental questions about the validity of characteristics used to distinguish the phyla of lower invertebrates. A sponge is defined as a ‘sedentary, filter-feeding metazoan which utilizes a single layer of flagellated cells (choanocytes) to pump a unidirectional water current through its body. Except for being sedentary, the cave Asbestopluma and presumably all Cladorhizidae lack these basic sponge attributes. In an extreme environment where active filter-feeding has a low yield, cladorhizids have developed a mode of life roughly similar to that of foraminiferans or cnidarians. Their feeding mechanism relies on passive capture of living prey and on transfer of nutrients into the body through intense cell migrations, the analogue of cytoplasmic streaming in foraminiferan pseudopodia. This may be compared to the emergence of macrophagy in abyssal tunicates, also accompanied by a reduction of the filtering system although in Cladorhizidae the result is more extreme, with a main body plan different from Porifera and resembling no other modern anatomical design.”In cases like that above, the lack attribution of phylum rank for these 'sponges' hides the fact that the Porifera may very well have given rise to an independent phyla.“Such a unique body plan would deserve recognition as a distinct phylum, if these animals were not so evidently close relatives of Porifera. Their siliceous spicules show clear similarities to several families of poecilosclerid Demospongiae.”
The web page points out clear evidence that some distinct phyla did in fact originate from others. (Arthropods from worms, for instance. This should be obvious to anyone who has ever seen a maggot or a caterpillar.) Furthermore, many of the first appearance dates in the fossil record are long after the Cambrian.