This is a serious issue, though. We use these terms as if they are primitives, and it's not clear that they are. Their essence ends up either circular or going back to some arbitrary description from a hundred years ago or so.
We are mostly likely "on to" something, with a real phenomenon lurking under the inadequate terminology (or inadequately defined terminology).
Of course this is a particularly extreme example (and possibly only applicable in one language), but it happens all the time. The terms we rely on fall apart once we interrogate them.
In my case, I'm currently going through about 300 languages to attempt to identify "serial verb constructions" and I'm having a really difficult time because the definition (which I have extensively researched and polished from a number of sources) seems completely arbitrary. In fact, my point in the end will be to argue against any deeper meaning of "serial verb construction" beyond just what certain languages seem to have on the surface, but to get there I'm trying to work within the definition and it's an interesting challenge.
Anyway, as for S as a vowel, why not?
If speakers of the (so-called) Khoisan languages can produce clicks reliably and contrastively at a volume effective for speech, I can certainly imagine someone producing /s/ as a nucleus, which is what vowels are. Vowels are the sounds that don't need other sounds (vowel) to support them in a syllable. In fact, we have a sort-of-word in English that has no vowels and just S as a nucleus: psst (as in "hey, psssst, look at me!"). And it would helpfully explain why S can anomalously go before stops. Of course this would contrast with a language like Spanish where s- must be preceded by a vowel for support, as in estudiar 'study', especial 'special', escuela 'school'.
I'm intrigued by this argument, but (not the fault of the argument itself) a little dizzy from all of the circles the terminology seems to drag us in.