Rey is already on the light side, the saber first calls out to her in TFA, and she actually knows how to heal as demonstrated twice on screen before the finale. Why wouldn’t Rey have been able to heal it herself?

The lightsaber suddenly being fixed when Kylo grabs it doesn’t make sense in-universe and would just come across as an error to a new viewer of the edit, and it doesn’t add anything thematically that Kylo wielding the blade in the first place doesn’t already do.

Always broken or never broken is my hard stance.