This sounds reasonable to me. I am most impressed by Brits, Aussies, Germans who can talk clearly in a US accent, from whatever region they are emulating. The ones who have not mastered the US accent, tend to speak in more of a gravely voice. I think Christian Bale falls into this category. However I heard him in an interview and could barely understand him when he used his natural dialect.
At the same time, I admit when I hear these actors speak with their natural accent, I am usually disappointed if I have bonded with them as a countryman/woman before I realize.

There are so many examples, but a few I knew about in advance:
- Andrew Lincoln (as Rick Grimes).
- Anne Hathaway
- Chris Hemsworth
- Damian Lewis
- Hugh Jackman
- Kate Winslet
- Henry Cavill
- Ian McShane
- Benedict Cumberbatch (An excellent job as Dr. Strange)
Now in reverse although I like Leonardo DiCaprio and Kevin Costner in several movies, I thought they sounded ridiculous using their natural accents in
The Three Musketeers and
Robin Hood respectively. But I’ve also noticed in several British productions, or with Brits in prominent roles, representing Italians (
Rome,
I Claudius), they use their natural UK accents without even bothering to emulate Italian.
As far as the OP question, they are drawn to Hollywood, still the world wide capital of movie making.