Quite aside from the question of whether low-carbohydrate diets are good for people, bad for people, or good for some people and bad for others, there’s the question of whether they’re economically sustainable — agriculture produces much more energy stored as carbohydrate than in other forms. So, some people have claimed that there isn’t enough land in the world for everyone to survive on a low-carbohydrate diet.
Soybean yields average 2.93 metric tons per hectare per year; world arable land is currently a bit over 48 million km², which is 4.8 billion hectares, about 11% of the world’s land area. Dry soybeans are 37% protein by weight. Multiplying these three figures together, if all current arable land were continuously planted in soybeans at current average soy yields, the world would produce 1.4 × 10¹³ kg of soybeans per year, containing 5.2 × 10¹² kg of protein, 680 kg of protein per person, or 1.87 kg per person per day — about 7500 kcal of protein per person per day.
However, soybeans are also 18% fat by weight, which would add another 910 g of fat per day per person, 8200 kcal, for a total carbohydrate-free yield of 15700 kcal. This is about six or seven times the human daily caloric requirement.
It seems likely that the yields from other arable land not currently cultivated in soy would be lower than current average soy yields, and also that sustainable farming practices would reduce yields modestly further. However, it seems unlikely that this would reduce yields by the factor of six that would be needed to make a zero-carbohydrate diet economically unsustainable.
Of course, soybeans also contain carbohydrates (30% by weight), but you can remove those before you eat them.
The reason that agriculturally produced food appears scarce is that most of it is fed to livestock, which converts most of it into manure. There are more efficient ways of removing carbohydrates from soybeans than feeding it to chickens or cows.
There may be a way to produce more protein per hectare than growing soybeans, but I don’t know of it; the reason soybeans are currently such an important crop is that they are the favored protein source for fattening up livestock.