Never. At first, chemical fertilizers do produce higher yields, but, over time, it takes more and more fertilizer to produce the same yield. Not only that but all chemical fertilizers leave salts which burn out the organic matter in the soil which in turn depletes the micro-organisms which enable plants to uptake nutrients. When this finally happens you end up with worn out soil. By using organic fertilizers you feed not only the soil but the plants as well. My garden has never had any chemicals of any kind applied in almost 20 years. I actually use less and less fertilizer each year and insect problems are minor to almost nonexistent. Here in the US many large commercial growers are going to a no till, organic fertilizer system. The price of chemical fertilizers fluctuate and is determined by the price of oil so when the price of oil goes up so does the price of chemicals. A couple of years ago organic pelleted fertilizer was quite a bit cheaper than chemicals.
Adding compost is great but it is very difficult if not impossible to make enough of it to supply a large area. But one doesn't actually need compost. Any organic substance will work if simply incorporated into the soil. A green manure cover crop works wonders. Many farmers around here plant their fields with it in the fall and then in the spring plow it under before planting time. This cuts down even more on fertilizer costs.
Leaching is another problem with chemicals. Chemicals do not adhere to soil like organics do. They dissolve and wash away much much easier than with organics, thus polluting ground water. Look at what is happening in Florida with all of that toxic algae they are experiencing. It is being caused by runoff of high nitrate chemical fertilizers being dumped into Lake Okeechobee and then being released into the ocean to prevent flooding. It is a major disaster and so far they haven't a clue about what to do about it.