Or maybe it is the more obvious reason: a TV series produced in the US in a nation that refers to themselves as Americans, and in the 1960s, long before the politically correct speak of referring to everything in the Western Hemisphere as "American" became common. If TOS was produced today, Spock probably would have been written as saying "Western US," instead.
In the US, American usually means " a citizen of the US, or something from the US" referencing nationality and this is normally understood within
the US, but outside of the US, in North and South America, people also refer to themselves as "American," usually in Latin American countries (IE Canadians usually still call themselves Canadian, sometimes NORTH American, because Canadians DON'T like being confused with being US Americans).
However, someone from say Colombia might say they are "American," but are actually referencing the fact they are from the continent of South America (IE North and South America are combined as the "Americas,") just as a French person might say they are European) and from that stand point, are equally valid, when they say they are "American," too. But this idea is confusing to some people in the US (or people in countries that mean US citizens, when they say American), as they say American meaning nationality, because it is easier to say American, than United Statesian.