
Could of wouldn't really be used in academic English because this is because academic English has a very specific set of rules for how to write and tends to follow traditions of grammar. In Southern dialects, could of/would of is really common. I'm from the South and heard it very often, and also, you are right that a linguistics major would be more knowledgable on this but I still wanted to chime with what I learned when studying dialects of English
You're right have is definitely what is considered "correct" in academic/professional English because that style of English has very specific rules on what is grammatical. In daily use though, it's very common for people to stray from academic English though. E.g. a lot of people say "who" instead of "whom" even if "whom" is the correct term academically/professionally no matter what part of an English speaking country you're from and very few care
Dialectally yes it is whats used in the south (Im from georgia! Grew up saying it myself) but whats used doesnt mean whats correct, grammatically it is incorrect. 'academic' english is a writing style/dialect of its own thats typically characterized by correct grammar but not directly correlated to whats right or not, like your example of who vs whom, who is still grammatically correct in most cases but whom is academic