Well the noted lack of research is one thing. Our research standard implies that E.L.L. may be a better place for unresearched questions, irrespective of whether it is true or false so that may account for much of the reason. More importantly though, note that this question is not asking why, but rather if the two are interchangeable. I see that at least one other question regarding the relationship between V and W was unilaterally closed by a moderator as General Reference. (Not "Please include the research…" mind you, but General Reference, so that is an old closure.)
Since I am on meta, I also feel free to posit some unproven guesswork: The pronunciation of each consonant is very distinct, and even if somebody lived in a region where the dialect rendered these indistinct, I suppose that they would at least understand that this is quite non-standard, if not only because other people would point out the distinct feature of the accent which renders these continents confusable. This is sufficiently demonstrated by the common word pairs of the top voted answer, and the fact that it mentions a 19th century Cockney accent, rather than any contemporary one. I struggle to think of any one word where the two letters sound just alike, including the granted examples.
Moreover, even in cases where its letters phonetically interchangable, the orthography of English is mostly settled, with most of the differences between American and Commonwealth orthography being in the termination. Normally, nobody would replace the c in cat with a k, even if the end pronunciation is the same. The answer to if is clear by means of commonly shared knowledge among native speakers.
Now I am ignorant to how the orthography of other languages works, but this seems like a question that is much more likely to be devised by, and hence useful for nonnative speakers just starting to learn English starting from a language with less rigid orthography.