The Caucasus is half in asia.

So if we are being most pedantic, then 'being from the Caucasus region' does not indicate if you are from asia or not.

Well Caucasian wouldnt be nearly as impactful as a word if it weren't for the USA.

Most of it's use comes from the creation of a 'white race' for use in politics/law/oppression/dehumanization.

And when that stuff began, remember the Italians, Irish, and many other now 'white' people were not considered 'white'. So being called European was out. Had to try and find a word that excluded the mediteranian peoples, since the bulk of wealth and power were mainly English, French, Germanic, and Dutch.

Note: and the people mainly responsible for the caucasian misnomering were not from Scandanavia and had yet to conflate 'white supremacy' with Aryans. And thus yet to describe ideal Aryans using Scandanavian features.