I know that martial arts are not exclusive to the region, so why (culturally, socially, etc.) has it become common practice to make the assumption that martial arts equate to Asia? Was it simply that there was more documentation from that region that supported a structured study into said martial arts? Thank you!
I think the answer is in the wording of your question - it's because "martial arts" is a literal translation of wushu, 武 (wu) meaning "military", 术 meaning "art / skill / technique".
In English, things like fencing, wrestling and boxing don't really have a similar shared name, although we might call them "combat sports" nowadays. For instance, in Le Morte D'Arthur, there are references to "knightly exercises" or "deeds of arms" (and, I suppose, lots of "torneying" - tourneying, competing at tournaments with lots of jousting and sword-fighting and even grappling) but those aren't exactly the same thing.