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Perhaps the best single scene in Pride and Prejudice is when Lizzy smacks down Lady Catherine de Bourgh, who has showed up at the Bennet family to declare that it will be entirely unacceptable for Lizzy to marry her nephew (Mr. Darcy). Being the drama queen that she is, Lady Catherine moans about pollution of the shades of Pemberley (Darcy's estate), and Lizzy mounts up and declares "He is a gentleman; I am a gentleman's daughter; so far we are equal." It feels like a uniquely modern moment: Darcy is related to nobility, Lizzy's family is in danger of losing their home, and she's asserting their right to love each other, if they like. But the truth is, it's not revolutionary: Lizzy's argument ultimately rests on a somewhat more flexible definition of societal rank than Lady Catherine's, but it rests on the idea that people of the same social rank are a match in marriage all the same.
That idea is expressed much more aggressively in Emma. (SPOILERS, BUT ONLY IF YOU'VE NEVER SEEN CLUELESS.) Despite Emma's devotion to her friend, Harriet Smith, throughout the novel, she ends up extremely relieved that none of her efforts to set up Harriet with various men work out when she learns that Harriet is illegitimate, because of course such illegitimacy would ruin a man who might be more appropriately paired with someone else. Mr. Elton, who behaves poorly, ends up punished by marriage to a woman who is as precisely boorish as he once acted. Emma doesn't particularly do anything to win over Mr. Knightley except listen to his criticism without arguing and have an appropriate social status.
Ultimately, I can't fault Jane Austen for writing social scenarios that essentially accord to the prejudices and norms of her time. The levels of education, the social situations, the chances for travel and study available to people of different social classes were different when she was growing up and writing. Those things do contribute to the success or failure of a marriage; they aren't irrelevant, even today. But fortunately, we have progressed to a point where we think it's a problem if folks don't get at least the same initial educational opportunities, and where we can see things like the marital status of people's parents as precisely as arbitrary as such factors are in determining someone's intelligence and moral character. Still, though, I miss the flash and the fire of Elizabeth Bennet declaring her independence and willingness to marry in the face of hilariously exaggerated disapproval. A girl who ends moving her husband into her house, and letting chance take care of the social and moral messes she's made behind her is no real substitute.