If you want to test ingroup relationships within Archosauria then you include all known hypothesized archosaurs (preferably as individual specimens and/or species) with a few closely related taxa (based on synapomorphy) as outgroups to polarize your characters. Isn't this what has been done?
It has been, but that doesn't work unless all those hypothesized archosaurs really are inside the ingroup. If the pterosaurs are outside (something I don't have an opinion on), making them part of the ingroup is guaranteed to screw up the entire tree. Perhaps only a few support values will be a bit off, perhaps the topology will be completely upside-down -- there's no way to tell beforehand.
So, to do an archosaur analysis, you have to include the pterosaurs, because they could be archosaurs; but to do an analysis with pterosaurs in them, you have to include all of the diapsid crown-group in your ingroup! (Not "all" as in "all twenty thousand species", but you still need to sample it all halfway evenly.)
And then it goes on. According to some, the turtles are crown-group diapsids. According to others, they're not diapsids at all. That means you have to include all of Sauropsida in your ingroup, and use Theropsida as the closest outgroup, just to test the position of *Vancleavea* properly.
And if you then take David Peters' doubts about the positions of caseids and various diadectomorphs seriously, or if you still take the hypothesis by Berman et al. from the 1990s seriously that the diadectomorphs are theropsids (based on very, very small matrices), your ingroup grows even more.
I have started compiling just such a matrix. It was originally planned to be part of my thesis. Now it might become part of my first postdoc, but even that is somewhat improbable now...
Caseids may share lots of characters with lots of different groups but which characters reflect true phylogeny and which are simply convergent? How does a large dataset with all tetrapods determine this better than a smaller dataset of only synapsids?
I think he thinks the caseids are not synapsids in the first place. (I have no idea why, they're screamingly obvious synapsids to me, but whatever.)
But autapomorphies tell you absolutely nothing about phylogeny. But autapomorphies tell you absolutely nothing about phylogeny. But autapomorphies tell you absolutely nothing about phylogeny. But autapomorphies tell you absolutely nothing about phylogeny.But autapomorphies tell you absolutely nothing about phylogeny.But autapomorphies tell you absolutely nothing about phylogeny...........do I need to say it again? :)
"Autapomorphy" just means "character state present in the first member of a clade and absent in its last ancestor". Every parsimony-informative character, thus, has a state that is autapomorphic of a clade.
What does not tell us anything about phylogeny are character states that occur in a single OTU and nowhere else in the entire matrix. They are of course autapomorphic of that OTU, but so are all character states that have convergently appeared in that OTU and in at least one other.
Vancleavea has numerous Archosauriform synapomorphies as well as a gamut of vertebrate plesiomorphies. As systematics we are interested in how high in the tree the synapomorphies place us. Where do you think Vancleavea is a better fit and based on what synapomorphies?
He thinks it's a thalattosaur; this was discussed here and on Tet Zoo a few months ago. (I still haven't replied to the last Tet Zoo comment, for lack of time.)
I think it would make a seriously weird thalattosaur, about as weird as it would be as an archosauriform, if not a bit more so.