The Doc wanted the rich guy’s death to look natural, from disease. That rules out just killing him right away.
The girl and her defenders had no intention of getting away. They were pulling a propaganda stunt. They knew they were going to be killed.
The post-apocalyptic people were only very occasionally raided by their enemies, until the events in this movie. There are lots of real-life tribes who live this way, being raided rarely, without defensive walls etc.