Also if you want to get the most out of your fertilizer you will automatically be trying to reduce erosion. No one wants to put investment into soil that is going to disappear or be lost.
There is also an increasing amount of regulation around controlling runoff of fertilizers in order to control water quality in lakes, rivers etc. Follow what is happening in Ohio and Lake Erie for example.
https://en.m.wikipedia.org/wiki/Haber_process
Roughly 50% of the nitrogen in average humans was extracted from the atmosphere using this process; it is well-established.
Still, if we had to change to renewable sources of energy to run these processes tomorrow,the price would likely jump so enormously that their value would be mostly in niche applications.
Seems like erosion has more to do with farming technique, independent of fertilizer use or not.
The soil erosion of the Dust Bowl area was addressed through improved technique. Fertilizers were not a key component of that.
The American Dust Bowl was a combination of things, but the frequency of tilling was a big part of it. Farmers now till at least one fewer times per year, which makes quite a bit of a difference.
It's complex, because our annual crops are almost all prairie soil plants, prairie soils are typically bacterial dominant anyway, but fungi typically provide a lot of the soil stability. Tilling pretty much kills all of the fungus, and the bacteria run wild breaking down soil carbon (fungal and crop roots).
If it wouldn't cause another dust bowl, a lot of farmers would probably plant only corn since its much more profitable.
Basically sand with a tiny bit of organic fluff.
Firstly sand blows away, secondly it doesn't hold water anywhere near as well. This means that you need more drainage channels, which means you get more runoff, which means you need more fertiliser.
_proper_ soil, with plenty of organic matter is both more porous _and_ able to absorb more water.
Other things can happen, too, of course: https://en.wikipedia.org/wiki/Dust_Bowl