Why did she have a trans-Atlantic accent?

You might perhaps better say: no one speaks like that ANY MORE.

Accents change over time. With the passage of 50 years for instance, a local accent can evolve considerably and unless there are recordings to prove it, most people don't notice the changes, since they often live through them.

That's for instance why Shakespearean dramas using upper class 20th century British accents are actually quite inaccurate. What did language sound like back then? Hard to say without sound recording. Generalizations can be made comparing rhymes in poems for instance, but accents are so subtle that they cannot be deduced easily.

You can do a search on YouTube & find videos of the real Earhart & hear her voice, then judge how accurate Swank's interpretation was. I think she sounds very much like actresses from the films of that time. Very Ginger Rogers-like to my ear.

JEFF:
That is one nutty hospital.