I feel like we need a different term to distinguish between "what-if" scenario AUs that take place in the same setting and AUs that build up a similar story in a different setting.

Regarding different-world AUs, I think the placement of characters into roles/occupations/positions/whatever is actually pretty important to them, and it should hold some similarity. Even if all the politically powerful characters don't simply get transported into government positions in a modern AU, they should still be in positions of authority so their main traits can shine. I mean, we'd all like to think our favorite characters would be the same no matter what, but circumstances really do shape a character. That's exactly where character development comes from-- it doesn't happen in a vacuum!