Arya must die. That way she truly becomes a nobody as the Waif.
Arya and the Waif are two sides of Arya struggling to take over the other. On one hand Arya torn between duty and compassion. The Waif on the other hand, single minded with what she needs to do.
One caveat with this plot is if Arya becomes a nobody as the Waif, then Arya is dead. We have lost another Stark but now have an instrument by which to further the Starks' cause.