I get the show wants to make the dagger important to her and it is sentimentally. But as a symbol, I (my opinion) can't see it being more than merely an object of value because the show already showed how easily she could have been parted from it if Elendil or Halbrand were more of an ass and kept/sold the dagger when they had their hands on it.
And since we're on the topic, Elendil didn't even notice he had the dagger stolen from him. Galadriel uses it later right in front of him, he doesn't seem to care either. Like, Halbrand stealing the dagger should have been the thing that put him in jail honestly.