It was understood that nitrogen reserves were quickly running out. At the time it was just as important for warfare as it was for food. Guano and sodium nitrate were such important recourses a war was fought over them. The Saltpeter War (April 5, 1879 – October 20, 1883) was fought by Chile and Bolivia over saltpeter reserves in the Atacama Desert. It was known at the time that Guano and sodium nitrate were finite, and that once exhausted it would lead to food shortages.
England and all civilized nations stand in deadly peril of not having enough to eat. As mouths multiply, food resources dwindle. Land is a limited quantity, and the land that will grow wheat is absolutely dependent on difficult and capricious natural phenomena... I hope to point a way out of the colossal dilemma. It is the chemist who must come to the rescue of the threatened communities. It is through the laboratory that starvation may ultimately be turned into plenty... The fixation of atmospheric nitrogen is one of the great discoveries, awaiting the genius of chemists. (Sir William Crookes - 1898)
Was it understood in fact that greater food production capacity would have this effect?
The idea that human population growth is potentially exponential was proposed by Thomas Malthus in 1798, and is referred to as the Malthusian growth model. At the turn of the 19th century the human population was starting to grow significantly faster, but agriculture was still dependent on bat droppings, human waste, and crushing up bones. We hit 1 billion people some time in the 1800's and we hit 2 billion before the industrial production of nitrogen fertilizer ramped up. It was understood the population was increasing very quickly. A result of many factors such as decreased infant mortality, better medicine, and more efficient agricultural practices (like using fertilizer).
But was there a time when anyone said, we need to be able to dramatically increase the world population?
I don't think anyone was saying it would be great if the human population grew exponentially. Cities were already over crowded, and at the turn of the century unemployment was very high. They were looking at the world around them, the human population was starting to grow exponentially, and they thought "how are we going to feed everyone?" What happens if you have a population that's growing quickly, but the ability to grow food can't keep up? The investigation into the industrial fixation nitrogen was a reaction to a looming crisis, and brilliant scientists figured out a solution.
I could see business leaders perhaps wanting more workers and more people to sell products to although I would guess it would be the food producers themselves who wanted cheaper fertilizer
It wasn't just farmers who wanted a cheap and secure way to source ammonia. It was used to make gunpowder as well as fertilizer. Germany was in a particularly bad spot they were importing 350,000 tones of Chilean saltpeter in 1900, and 900,000 tones in 1912. Then World War 1 started, and allied blockades stopped the import of saltpeter. The Haber–Bosch process allowed them to continue fighting even without an external supply.