I think that even though this answer certainly explains the issues with it, the original construct in the question of "Dragons are big, green, and eat people" still sounds the most idiomatic / least clunky to me. I agree that if you parse it completely literally the last part does equate to "are eat people" which is strange, but I feel that, as with a lot of other constructs in English, readers parsing it the way it's intended rather than to the letter is going to be more common.