Alternately, riffing off of your idea of Rey killing Kylo, it could be that Palpatine is seeking a suitable host for his spirit. Palpatine wants Kylo to kill Rey just like Snoke wanted, for this would turn Kylo irrevocably evil and make him a willing host for his evil spirit.

Alternately, Kylo may say in the hangar that Rey is already suitable as a host for Palpatine, which is why Palpatine told Kylo ‘she isn’t what you think’. Rey killing Kylo would merely be more confirmation that she is the one who will be Palpatine reborn, joined to him deeper than blood.

For this idea we could move Palp’s dialogue about his Sith spirit back to the end of the film as it wouldn’t apply to Kylo in that moment, and just fill Rey in on this whole procedure during the hangar scene.