I think that's very true. The mentally independent Elizabeth is the easiest for a modern woman (or man) to relate to. I think a lot of people have trouble connecting with, say, Fanny Price less because she's shy (we've all had moments of shyness, if not more) than because her mental worldview is one we don't share and often find claustrophobic, or to Emma Woodhouse because we can't quite stomach what to us is clearly snobbery, though most of her contemporaries would call it a rational evaluation of the world. They're simply operating according to rules we no longer know and what seemed natural to JA's audience can seem stilted. It's hard to recreate on the page.
That said, I think a careful author can do some research and thread that fine line to some degree. Some of the most obvious rules can be followed (chaperonage, for example), and some of the most important assumptions (that a wife would be completely dependent on her husband and needs to be sure of his character, say) born in mind. Some of it depends on the ambition of the author. Sometimes you just want a nice story in a Regency sash, and that's OK. But I would argue that most of the best fanfics try to engage with that worldview.
That said, I think a careful author can do some research and thread that fine line to some degree. Some of the most obvious rules can be followed (chaperonage, for example), and some of the most important assumptions (that a wife would be completely dependent on her husband and needs to be sure of his character, say) born in mind. Some of it depends on the ambition of the author. Sometimes you just want a nice story in a Regency sash, and that's OK. But I would argue that most of the best fanfics try to engage with that worldview.