Before the introduction of western diseases, North America had a much larger population than we are taught in our Manifest Destiny classes. It's fair to say that the population here is about one order of magnitude greater, but if we ran the Mississippi watershed the way the Chinese managed the Yangtze [1]? Or the tribes of California? [2] We'd still be doing pretty well without anhydrous.
Again, though, we'd be eating a lot more beans. We should be eating a lot more beans. And nuts.
When Polynesians settled Hawai'i, they brought a couple dozen species with them (canoe plants) and found the Koa, a nitrogen fixing tree. When Europeans occupied Hawai'i, they brought a few more, including the monkeypod (another nitrogen fixing tree) as cattle fodder. The bean pods are high in protein.
> "However, in the soil of natural ecosystems, nitrogen occurs predominantly as proteins."[3]
Everyone talks about the magic of nitrogen in plant and soil biology, but at the end of the day, it's the protein cycle that matters. "Feed the soil, feed the plant"[4] requires polycultures instead of monocultures in order to work, but we could do it. We would have done it. George Washington Carver wanted to do it [5] but he got outmaneuvered by industrial agriculture (and structural racism). In another world without anhydrous he probably would have found more success.
Tl;dr: Things would look very, very different but not necessarily smaller - or worse - if not for chemical fertilizer, and we may have to get to that world soon if we want to keep on breathing and eating.
References:
1: Farmers of Forty Centuries: Organic Farming in China, Korea, and Japan, F. H. King
2: Tending the Wild, M. Kat Anderson
3: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2393761/
4: Roughly any book on Permaculture
5: My Work Is That of Conservation: An Environmental Biography of George Washington Carver
China was doing pretty well for itself for millennia with intensive terracing and silt harvesting. They have fields that have been under cultivation for four thousand years. We can barely manage four hundred.
And pre Columbian California was agrofoerstry from sea to foothills with seasonal migrations.
Without anhydrous ammonia we would have a diet much higher in legumes and lower in staple starch, which is probably killing us anyway. A more efficient source of high fructose corn syrup doesn’t inspire confidence in our future.
Corn still uses far too much water for us to sustain indefinitely.
[Edit] We would also be using more perennial crops, which don't have to build up an entire plant from seed every year. More efficient, as long as your form of civilization does not involve moving into new areas every ten years.