Aiden had no intention of shooting the defenseless Sister Neve here; it wasn't a matter of principle, but simply because it was unnecessary.
He had only two purposes for getting involved in this conflict: one was to eliminate the Harvest Mother Cult that threatened Rose Iron Prison, and the other was to take advantage of the situation to attain some divine abilities. As long as his objectives were met, he would not do anything superfluous.
Now that the Harvest Mother Cult was as good as annihilated, as long as Sister Neve here transferred all her divinity to her, she would not be able to use the divine word of "Reproduction." Once in Rose Iron Prison, she would be no different from the prisoners in the core area.
And there were indeed benefits to keeping Sister Neve alive.
Sister Neve was a saint of the "Reproduction" authority, and her understanding of it certainly far exceeded that of an ordinary person.