[Stephen Turnbull's: The Ninja, an Invented Tradition?] (https://pdfs.semanticscholar.org/530c/a6033ff2379c4837081199ba088111840ebf.pdf) Which is him admitting his old book on ninjas were full of mistakes.

It's not a book. But it's the most academically sound piece.

"Autonomy and War in the Sixteenth-Century Iga Region and the Birth of the Ninja Phenomenon" in War and State Building In Medieval Japan. Is another good one.

Basically there's a lot of problems with the popular, traditional depiction of "ninjas". "Shinobi" and people who did scouting/spying existed, but they were often regular members of the army/society who just happened to do those thing, not anything like FBI/CIA/KGB/Seals/SAS or whatever. This question is like asking what was the function/influence of James Bond/Jason Borne on western society, when any impact's pretty restricted to cultural depictions.

And no I'm not well-versed enough in the cultural depiction of ninjas to give an answer on that sphere.

/u/NientedeNada wrote about a lot of the problems with ninja tradition here, here, and here, and I gave some examples demonstrating why ninja stories in the historical are problematic here, here, here, and here