But Palpatine created the Skywalker bloodline, didn't he? Wasn't it revealed in canon comics that he was the one behind Anakin's spontaneous conception?
If Ben dies but succeeds in destroying Palpatine, then Palpatine will have been destroyed by his own, flawed creation - and yes, the Skywalker bloodline will have ended.
However, the Skywalker Legacy that Luke, Leia, Anakin, and Ben created - that is not inherently affected by Palpatine's dark side powers - will live on indefinitely, starting with Rey (hope).
This make the most sense to me. It also allows both Ben and Rey to play extremely important parts to the overall story beyond both fighting in the final battle.