I'm a writer and indie game dev of indie games with cum in them. One half of @BPGames. Most recent project - Opportunity: A Sugar Baby Story.
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@zippity - goofy porn game screenshots
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The prevailing theory is that the D2 dev team, which is almost always short on time and resources due to the game's (relatively-speaking) breakneck pace of content releases, has very little in the way of direction for the voice actors, meaning that they all kind of found their own voices that sounded good for their characters which work in a vacuum but raised questions once they started having familial relationships. Which is to say, whoever had the final sign-off on the various Bray family member's VO recordings either didn't have time to stop and think whether the accents all made sense, or they DID notice but didn't have the time or budget to record new takes
It's also very possible that back in D1 when Elsie was just The Exo Stranger it wasn't set in stone that she would, in fact, turn out to be Elizabeth Bray
or she's just one of those people who studied abroad for two weeks in college and came back with an accent
I think the last point is the correct one. Remember, Destiny 1 original story was a cobbled together mess. They scraped bits and pieces of the unreleased story(where Exo Stranger was an assistant to Osiris, who was involved in the story) to make the abomination that got released in the end.
The whole "Exo Stranger is actually Elsie Bray" likely wasn't set in stone until way later. Hell, even way into Destiny 2, Luke Smith said that "the Exo Stranger's story is finished".