In order to provide vegetarians with dairy products, cattle must be bred. But only females are needed for milk. The males will not be sent off to live out their lives happily in green pastures; apart from a few kept for breeding, they will be slaughtered. The same goes for male chicks in egg production. The bodies will have to be disposed of, either as landfill or by burning, both of which have health and ecology implications.
Apart from environmental issues, this also removes any moral high ground from vegetarians. What's more, in Veggie World, anyone who eats meat but not dairy would be forced into veganism. That's not just lactose intolerant Westerners but a large proportion of the population of Asia.
Veganism may be the only true moral position regarding the exploitation of animals. But it has its problems as vegans don't eat honey. The bees that produce honey also pollinate crops as well as wild flowers and other flora essential to a healthy eco-system. Wild bees are not enough. So if we all became vegan, the planet would be headed for disaster unless we all kept bees as pets (not such a bad idea).
What would Veggie World be like?