Logic Patrol/Spoiler Alert

I think Viklander is an excellent actress however I have a problem with the logic in this film. Feel free to educate me. So after Lara meets up with her father in the cave she proposes that the two of them escape the island with the assistance of the cell phone. She makes no mention of saving any of the slaves. Her father will not leave the island because Lara has let his notes slip to the villain. With these notes the villain can locate the entrance to the tomb. Although later it is shown that even with these notes the villain is stymied.

Anyway, when Lara sneaks into the villain's camp she finds herself alone with him. She could kill the villain with the bow and arrow and make off with the phone and the notes... End of story. But instead she starts a full blown exchange with the small army of the villain's crew. Why? She could have had the means of escape and the copious notes.......