In fact, the comprehensibility of the entire ST rests on Leia being a Skywalker.
How so? Kylo doesn’t need to be a Skywalker to be a Vader fanboy, and he still comes from two important lineages, if you’re worried about it stealing from Rey Nobody.
She’s the other hope, if Luke should fall to the darkness. And she was that hope, when Luke abandoned the galaxy she was there forming a Resistance against the will of the Republic and preparing to fight the First Order. Luke also had the strength to face Vader and the Emperor because he knew she could keep the fight going if he failed; to quote Luke in The Last Jedi, he knew that if he died he wouldn’t be the last of the Jedi.
It does rest on her as much as him being a Skywalker.