I’m absolutely baffled by the conclusion that Rey has no character arch/development/growth. This might be the case in The Force Awakes, but doesn’t remotely hold up where The Last Jedi is concerned.
Rey starts out as a character with a huge lack of self-worth, has abandonment issues, and wants nothing more than a place to belong. A sense of family. She has learned to be self-reliant to survive, but emotionally defines her self-worth on how she is needed by others. She’s eager to assist the Resistance because someone finally needs her, she clings to Han Solo as a surrogate father because he’s one of the first people ever to see value in her. It is very much a defining trait for her, although this plotpoint isn’t resolved until the following film.
The cave scene on Ahch-To, like the scene where Luke enters the cave on Dagobah in The Empire Strikes Back, is a key scene. Both characters in these scenes are confronted there with their bigegst fears, which, as Yoda explained, is the first step towards the dark side. Luke’s biggest fear (although he doesn’t grasp why yet), is that he’ll be corrupted and become a new Vader. Rey’s biggest fear is that there’s no place she belongs; that she’ll solely have to rely on herself forever.
It’s partly why she was so desperate to find Luke and restore the Jedi in the first place, and it’s probably why she was so susceptible to Snoke’s pairing her up with Kylo too. Her fear of abandonment and lack of belonging is her prime motivator. It’s exemplified by how surprised she was anyone even bothered to come back for her, when she ran into Finn on Starkiller base in The Force Awakens.
Kylo’s revelation that her parentage turns out to be meaningless (which she knew deep down) isn’t robbing her of motivation, it’s a confirmation of her biggest fear. It doesn’t render anything moot: it actually ups the ante by making Kylo’s subsequent offer to join her at his side so much more tempting. Joining the dark side would be a resolution to everything she wants in one fell swoop: She’ll have her belonging through a grand role in the universe, become the polar opposite of a ‘worthless’ scavenger, and have a partner who she’s already greatly in synch with, someone who desperately wants her at his side and can train her in the ways of the force as well; someone who can finally show her her “place in all this”.
She refuses. Not out of a need for survival, but because she feels her own moral code supersedes it. By resisting Kylo’s offer, she resists the fear of abandonment that will lead her directly to the dark side. And she doesn’t rely on the (failed) dogmatic Jedi teachings either: she follows her own values, and decides to save her new friends. Not because it’s the easy thing to do, but because it feels like the right thing to do.
It could be argued it’s the first decision she makes in both films that isn’t motivated by her fears in any way.
It’s the culmination of a hero’s journey through self-acceptance.