As Etymonline suggests, the use of “a” meaning “have” in expressions like “should have” (shoulda), “could have” (coulda) and “would have” (woulda) were almost standard usage until the 17th century:
verbal phrase, 1902, representing casual (American) pronunciation of should have.
- The use of a or 'a to represent a loose pronunciation of have as an auxiliary verb is attested from mid-14c. and was all but standard English until 17c. (also preserved in coulda, woulda).
Similar expressions like gonna (going to) and wanna (want to) have a less clear origin.
- Wanna and gonna are frequently used in speech in informal colloquial English, particularly American English, instead of ‘want to’ and ‘going to’. You will also see them used in writing in quotes of direct speech to show the conversational pronunciation of ‘want to’ and ‘going to’.
Gonna appears to have similar earlier usages in Scottish dialect (ganna, gaumna) but it is not clear if they are related to the AmE ones:
representing the casual pronunciation of ‘want to’, by 1896.
attempt to represent the casual pronunciation of ‘going to’. In Scottish dialect, ganna, gaunna recorded from 1806.
Going to - Casually pronounced form : I'm gonna veg out tonight (1913+) - (Dictionary.com)
According to the above sources, the cited expressions appear to have rather old origins, but they emerged, or probably reemerged, around the end of the 19th century/beginning of the 20th century mainly in American English.
Is there evidence that the older original usage of shoulda, coulda etc. actually influenced by assonance the later expressions like gonna and wanna, or have they unrelated origins?
Is there a plausible reason why this “a” usage emerged mainly in AmE?