Why not use 먹이 for human food, too?

Koreans generally use 먹이 to refer to animal "food," "feed," or "prey," and 음식(飮食) or 먹거리 to refer to human food, but why can't 먹이 also be used to refer to human food? I am asking because 먹거리 seems to go against grammar rules since -거리 is usually added to nouns, not verb stems. Here are some acceptable -거리 nouns:

• 국거리........foodstuff for soup
• 김칫거리.....foodstuff for kimchi
• 반찬거리.....foodstuff for side dishes
• 저녁거리.....foodstuff for dinner

거리 is a noun meaning "material" or "makings," so if it is used with a verb like 먹다, then people should say 먹을 거리, not 먹거리. However, why not just say 먹이 for both animal and people food? If it is possible to say 쇠먹이 (cattle feed) and 말먹이 (horse feed), why not 사람먹이 (people food)?

On a completely different topic, while looking up one of the above words in my dictionary, I came across 사람 멀미, which means "sickness from being in a crowd." I had heard of 차멀미 (carsickness), 뱃멀미 (seasickness), and 비행기멀미 (airsickness), but had never heard of 사람 멀미 (crowd sickness).