If I contrasted indigenous Americans with "European" culture rather than a "western" one, you would completely understand the meaning and it wouldn't be a big deal.
Not exactly.
I wouldn't know if you mean "European culture" in the sense of something unique continental European (the way Europeans have unique cultural traits different from US traits, e.g. analytical vs continental philosophy), or the shared western culture Europeans and US Americans, and Australians, etc have?
That would sound to me like a deliberate misread in the same way that taking "west" literally is to you. You would know what I meant to say, and so would I should you say it the other way.
>You would know what I meant to say
Not really, only with extra context/explanation.
It's common to divide US/European culture (even though both western), or to include Japan in the western culture (even though not in the west, and their culture is not European of origin -- west in that sense is more like "westernized").
Not really. Then we'd be changing terms established for centuries, that most people understand in their two contexts (geographical and cultural), with some new words we'd have to explain every time we use them -- so making things worse.