Why do Koreans say 같은 양의 물 instead of 같은 양인 물?

I was doing some research and came across the expression 같은 양의 물, which means "the same amount of water." For some reason, it got me wondering why Koreans say 같은 양의 물 instead of 같은 양인 물. They say 같은 양이다 (the same amount), so why not 같은 양인 물? I searched Google for "같은 양인 물," but got not even one hit. Even when I tried searching on 양이 같은 물, I got only one hit. What's the deal?

Whenever I see the possessive marker 의 in a phrase, it makes me think it might be a Koreanized form of a Japanese or English phrase, and I try to change it into what I think would be a more traditional style of Korean by removing the 의. For example, if I saw the phrase 같은 나이의 사람, I would want to change it to 같은 나이인 사람 or 나이 같은 사람, but according to Google, 같은 나이의 사람 is more popular with Koreans. What's the deal?

I think more and more Koreans are using 의 phrases because more and more Koreans are studying English, and 의 phrases seem to be a more direct translation of English "of" phrases. For example, 같은 양의 물 is a word-for-word translation of the English phrase," the same amount of water": 같은(the same) 양(amount) 의(of) 물(water).

I am not sure, but it seems like 의 is killing off traditional Korean expressions, like a weed kills off flowers in a garden. Maybe phrases like 같은 양의 물 (the same amount of water) and 같은 수의 물건 (the same number of items) are correct, but there is something about 의 that makes me dislike them.