I feel like the show pretty quickly establishes that Galadriel is kind of insane. Her first scene is climbing a giant icy cliff, then pushing her struggling men through a blizzard on the vague chance of finding a clue to help advance her centuries long revenge mission.

How would they inform the audience in a better way?

Trying to swim across the ocean is exactly the kind of crazy shit a First Age elf would do, this complaint has always confused me. Its not like she even made it.