I've been reading about this tonight. Some of the places that try it say the cattle are stressed and lose weight, and it requires huge amounts of supplemental feed. And then the land doesn't seem to do any better than under conventional grazing. I think there are several problems; some with his theory and some with those testing it.
The impressive before-and-after pictures in his TED talk IIRC were taken 20 or 30 years apart. That's both good and bad. (of course it is) It shows that for whatever reason desertification in that area was reversed rather than get worse as it usually does. How long were the USA tests? Were they objective?
Has anyone tried using buffalo? Or maybe Texas longhorns if you must use cattle. They also keep saying 400% increase in number of cattle. 400% increase in herd density makes a lot more sense; if the land will support 100 head of free range cattle, you don't put 500 head on it, you confine the 100 to 20% of the area at a time (that doesn't sound right; you probably want a much smaller area, at least a first.) But the 100 head should remain the same until the land starts to heal and its carrying capacity increases.
The enviroweenies have too much invested in the Global Warming Climate Change meme, and are convinced cattle are the devil. Cargill, Monsanto, ADM, the US Dept of Agriculture, the US Dept of the Interior, and other big corporate interests (see what I did there?) have a good thing going with the current system and will try to derail any disruptive technologies. Even the United Nations has a conflict of interest; the crises in Africa gives them relevance so they don't want anything actually solved.
Mr. Savory (I thought it might be Dr. but it's not) explained away a lot of questions using handwaving rather than real answers. I give him a pass on the Climate Change issue; throw the weenies a bone and then say you have a solution. Topsoil does sequester a lot of carbon, but his "people who know far more than I" line without actually naming any of those people sound like he was making up statistics.
ETA: one more important thing I forgot to mention; he ignores the part where the animals themselves eventually return the the grasslands when they die. When raised for beef, they'll be harvested and taken out completely of the system in less than 2 years.
It looks somewhat legit and way overhyped at the same time to me. Maybe you have to hype it up to get anyone to listen. Has anyone verified those pictures he showed?