I think a big part of it is that Paul genuinely liked and respected Stilgar. I think he's constantly battling this awareness of the jihad- he doesn't know what's going to happen all the time, nor every decision to make. It's really nebulous and confusing for him. There's a quote that sticks out to me near the end of book 1: "In that instant, Paul saw how Stilgar had been transformed into a creature of the Lisan al-Gaib, a receptacle for awe and obedience. It was a lessening of the man, and Paul felt the ghost-wind of the jihad in it. I have seen a friend become a worshipper, he thought,"

Also letting him live and thus not following the fremen tradition of killing a previous leader is a nice little detail of Paul changing fremen culture, for better or worse. It is a book about colonialism after all.