Have you actually tried it? It's feasible if you occasionally eat some eggs, but if your diet is mostly based on eggs you simply won't have enough. The main reason of animal abuse on chicken farms is scaling the supply to reach the demand.
Not even speaking about the fact that it's pretty difficult for somebody who lives in a city and doesn't own a car.
Not even speaking about the fact that it's pretty difficult for somebody who lives in a city and doesn't own a car.