As many as 80% of the N atoms in your body were fixed artificially by the Haber-Bosch process. Natural sources, using pigeons or not, are not up to the task.
Birds are fairly high up the food chain, and their excrements are very rich in various nutrients, including nitrogen, phosphorus and potassium.
The Haber Process is faster but requires a lot of energy, and provides no phosphorus or potassium, so you have to source it elsewhere. Also it requires no technology and can be installed pretty much anywhere.
ps: I recommend we let current humans die of old age, and make less new ones. Not attempt to get rid of humans already here.
Mankind has survived just fine since ancient times without burning anywhere near the amount of fossil fuels burned over, say, the last 200 years.
With wind and solar, we are an the cusp of extremely cheap electricity.
>> is to simply have less people.
Feel free to follow your own advice.
Pigeons transport N from non-farmed areas (like forests) to farmed areas (where the towers are).
Sure they are. Just not on the current scale (for the current processes and preferences). It raises an interesting question about how many people the earth can sustainably support though.