The problem is that for those who don't already know this, these article are typically not that educational, and that for those who already do, any potential advantage of these pigeon tower is not explicitly elucidated either.

For example I can come up with self-concocted explanations why this is senseless in the sense you describe: i.e. fundamentally the bird is not a nitrogen fixer, so it ate the fixed nitrogen compounds from which the compounds in its faeces derived.

On the other hand I can come up with explanations despite its not being a nitrogen fixer why it still might be a net positive decision: perhaps the land has some insect pests anyway (pigeon towers or not), so that having the pigeons around results in them eating predators of your crop, while recycling those predators into useful nitrogen compounds...

The problem is that I know its just a wild guess I make.

Ideally we would read an article and understand under which conditions the pigeon towers make a net positive versus a net negative.

I am not trying to take a dump on the article: I'd rather know such structures existed and know I don't fully understand when they make sense than to know nothing about it at all... understanding must start somewhere.