i don’t think an explanation is necessary, but i think there’s something that could add value to the saber, it’s a direct visual parallel, maybe kylo could see the cracked and unstable skywalker blade in his vision with vader’s helmet, and it all spins in the same direction, cracked sabers, cracked helmet, pull to darkness, pull to light.
it could be something in the likes of:
Rey: I see through the cracks in your mask. You can’t stop seeing what you did to your father.
Kylo: I saw you tried to repair my family’s saber. But there are cracks that can’t be restored.
EDIT: also, the skywalker saber is an important plot point in the previous movies, i highly doubt that anyone, specially kylo, wouldn’t have anything to say about the legendary skywalker saber being cracked and unstable just like his