In Chapter 46, when Emma hears that Mr Churchill has given his consent to Frank and Jane's engagement with little persuasion:

"Ah!" thought Emma, "he would have done as much for Harriet."

Now admittedly this is before the scales fall from Emma's eyes about the object of Harriet's affection, an epiphany which seems to make her former conviction, on no evidence, that Harriet is a gentleman's daughter evaporate. But does anyone think, in the event of Frank actually caring for Harriet, it would have been that easy?

Mrs Churchill was the real problem, of course, but Mr Churchill has pride - Mr Weston describes it as a quiet, indolent, gentleman-like sort of pride. But even degree of pride might be enough to go against Harriet. It is one thing for him to give his consent to Frank's marriage to Jane. Jane is definitely the daughter of a gentleman - every officer who held the King's Commission was automatically a gentleman - and his lawfully married wife, herself the daughter of a clergyman, another gentlemanly profession. She is moreover beautiful, socially adept, intelligent, highly educated, talented and accomplished and (except in Emma's mind in earlier days) she has an impeccable reputation. She has no money, but the Churchills don't really need a large dowry. Jane is quite capable of making a good chatelaine of Enscombe.

On the other hand Harriet is the daughter of a man who may or may not be a gentleman and a woman to whom he was never married, which in itself greatly reduces any chance of her having been a lady. Her father, whoever he might be, has no wish to acknowledge her. She is beautiful but her manners, though improved by Emma, are still youthfully gauche. She is not intelligent and has received an indifferent education and a modicum of accomplishments at an obscure and unfashionable (sorry, Mrs Goddard) boarding school. Her reputation is tainted by her illegitimacy - which is desperately unfair, but was the prevailing view at the time. She might possibly have a dowry. Somehow you can't quite see her as the mistress of a great house.