Of course, we'll never see EVERYONE be vegetarian. Nor should they. Before I get into why, let me preface it by first saying: I went vegetarian for a few years after meeting my vegetarian girlfriend. It wasn't too hard for me since I was mostly raw vegan at the time anyway.
Cows are good for more than just beef. Milk is another animal product derived from cows. If everyone went vegetarian, what would we do with the cows? Use them just for their milk? That would make milk, cheese, and butter a lot more expensive.
If we stop using animals for profit there won't be a financial incentive to raise them. Cows are domesticated versions of the extinct aurochs. Without humans cows would likely cease to exist. They'd go extinct because they've lost their wild animal instincts.
The best thing we can do for cows is to raise them humanely. It turns out that it works out better for us and the planet too, if we raise them naturally. Grass-fed cows and chickens are higher in long-chain omega-3s, which are essential to good health and lacking in vegetarian diets. You can get short chain Omega-3s in seeds like hemp seeds and chia seeds, and in walnuts and other foods, but the body has to convert it into the long chains. Unfortunately, not everyone's body is efficient at converting the short chains into long chains. So even if they're eating enough short- chain omega-3s, they may not be getting enough long-chain omega-3s, like DHA and EPA.
Plus, by raising cattle properly we can actually restore nature, including deserts! Watch Allen Savory's TED Talk to see what I mean. Yes, raising them in factory farms is terrible for us, the animals, and the planet. We need to get rid of that. So THE KEY is to reduce animal consumption by eliminated factory farming. How do we do that? Well, if we'd stop subsidizing GMOs, which are largely grown to feed animals, that would be a great start.
So while everyone being vegetarian may seem noble, it's fanciful and probably not the best thing for the world.