Caring about animals is one thing, but having the money to do so is another.
You're right, there are a lot of dairy cows, but you also have to factor in you'll need land for: horses, sheep, goats, cows, pigs and chickens. Given the high numbers we currently have of these animals, that would require reducing the stock across the world to a very small amount, meaning that inbreeding would occur after a couple of generations. Then you need to find someone who is willing to give up their grain, and thus money, producing land for these animals to live out their days, all at this person's expense.
I do not envisage a world full of vegans who care, to be honest. I don't see it happening. I reckon veganism will ultimately become a social pressure that will start to influence governmental policy, etc. until the world is either forced into veganism or vegetarianism. From that point on, it will just be the norm, but I don't ever see every person actually caring about the individual welfare of every animal, especially where money is involved.