In Googling this question, I found out about Arrernte, which is arguably VC(C). Are there any other languages which have been argued to be a VCV language? And is there any reason why they're so rare in the first place?
The main reason is that the claim about Arrente is not self-evidently true, but that language has the distinction that a credible argument has been made. If you had asked "Why have so few such persuasive arguments been made", I would point to the larger problem of making persuasive arguments in phonology (an analogous question is "why have so few languages been shown to have synchronic final voicing". The immediately next reason, intimately tied to the first, is that by default it is assumed that all languages have CV syllables, and extraordinary proof is demanded of the existence of no-onset languages. A third reason, connected to the second, is that it is widely assumed that all segments are parsed into syllables, but there has never been a particularly compelling reason for that claim (and is not universal, see Bagemihl's analysis of Bella Coola). Given VCV, there has been a purely theoretical assumption that C has to be in some syllable, so naturally and Jakobsonianly we assume the C is an onset (not a coda, not unsyllabified). A fourth reason is that the argument in Arrente is fairly theory-specific and might be overturned with a different set of assumptions. This was done by Topintzi & Nevins 2017. Fifthly, kind of drawing on all of these points, the positive evidence that C in VCV is an onset in other languages is weak, but the evidence that it is a coda is also weak, perhaps weaker.
The final consideration would be, what is it about C+V that encourages the idea that there is some tighter grouping? I think it is a phonetic fact, not a phonological fact, that tightening the timing between C and following V results in an easier-to-parse distinction between C and V, especially in the form of a loud consonant release. This may be the functional explanation behing the preference for rightward parsing of C into a tigher relation with the following V.