It's possible to raise cattle in this way, but that doesn't mean that if you buy beef, any of it will be raised in that way. If you buy cattle that's grazing at all, you're paying extra for it. It's not possible to satisfy more than a fraction of current demand with ecologically friendly grazing. It's not grazing I'm referring to which is resulting in desertification, but monoculture agriculture which is used to support the livestock.
I notice that a large fraction of Effective Altruism people are vegetarian. This makes sense: in general Effective Altruists take moral issues seriously, even when that means changing your lifestyle. I'm not sure it's a good balance, though.
One way to think about this is to convert it into money. How much would I need to be paid to give up eating meat? All animal products? How much money would I need to spend on myself to be about as happy as I would be with less money but continuing to eat animals? I'd probably be willing to go vegetarian for about $500/year, vegan for maybe $2000/year.
It turns out you can probably pay to convince other people to be vegetarian much more cheaply than that. I estimate the cost of a vegetarian-year at $4.29 to $536 while Brian Tomasik estimates $11 with better methodology (which I looked at). This is by placing ads on facebook for a site where people can watch an animial cruelty video and ideally become vegetarian or vegan.
If you would get more than $11/year worth of enjoyment out of continuing to eat meat, why not give $11/year to convince someone else to not eat meat for you? Or give $50/year and be on the safe side?
(While you're giving money, you should probably give it to the organization that you think will do the most good with it, which I think is probably one of GiveWell's top charities. The nice thing about money as opposed to actions is that it's easy to redirect.)
I also posted this on my blog.