Why do you think they suffer more? And the amount of time spent on farms isn't the critical issue here, rather the amount of food that can be created per hour of life. Dairy is more efficient than beef production, that translates into less environmental damage and more food energy created per hour the animal is alive. And dairy cows are, in most cases, better treated than cows raised for beef....the farmers have more of a invested interest in their health.
Well I guess it can be one....its just a bad one. The conditions on factory farms can be used to argue against that form of dairy or egg production...but they aren't an argument against dairy or egg production in general. You can, and people do, produce dairy and eggs in other ways.
Suggesting that dairy and eggs necessarily involve animal exploitation is a different sort of argument, but if one thinks all animal exploitation should be avoided that is going to lead to the avoidance of pets, rescue animals, etc as well. Not to mention it would decimate our ability to grow nuts and fruits. This sort of argument makes more sense, I think, but I'm not sure how to make sense of the consequences.