Could the following question be considered on topic on the Linguistic site? https://english.stackexchange.com/questions/394563/why-are-expressions-like-gonna-wanna-and-shoulda-american-english
Probably not, because it is about the usage in a specific language, English.
OTOH, questions about contraction as a common linguistic phenomenon are not too rare on this site.
So, if it is primarily about a single language, then it make sense asking it at a place where users familiar with that language.
If it is about other aspects of contraction which may affect multiple languages, writing systems, and cultures, or perhaps some issues of automatic processing of these (NLP/CL), then Linguistics must be a better place.
It would be on topic. Although it is about just one language, there is no rule against asking a question about a single language. Unfortunately, there is substantial confusion over the "language specific grammar and usage questions" rule, and is not spelled out in any way in the help center. This rule being only visible as an unadvertised close reason, you really can't predict whether a question about the linguistic history of a single language will get closed. That close-reason also says "unless primarily concerned with linguistics rather than usage. There are many language-specific sites where such questions are welcomed; see: http://stackexchange.com/sites". A possible implication of that second statement is that questions about the grammar of a single language have to be directed to a language-specific site. I don't think that's what the rule is, and I occasionally rant about that problem, but that is just the way it is.
This is not a question about "usage" which is what I think the "language specific" rule is about. That is, it doesn't call for prescriptive judgments about proper English or what's good style. The reasons for those patterns are linguistic, especially having to do with lenition of /t/ in American English and some UK dialects. It is, however, a toss-up whether you'd get a good answer in either place, that is not an answer based on "why it might make sense", but one grounded in a thorough understanding of the documentary evidence.
So there are different opinions about the matter.