Mr. Hurst is like a shadow or thin air, saying nothing and doing nothing more than eating, so he has no use in the development of the whole story. Why does the author put such a man in the novel?
One of the things that Austen is doing in Pride and Prejudice is considering what makes an ideal marriage. Her answer is mutual affection, respect, and support; and a generous income.
To dramatize this thesis, Austen portrays a range of marriages that fall short of the ideal in various ways, to contrast with the ideal marriage of her heroine. There are the Bennets, whose felicity was spoiled by Mr. Bennet’s financial imprudence and Mrs. Bennet’s consequential anxiety about the prospects of their daughters. There are the Collinses, where Charlotte “sacrificed every better feeling to worldly advantage” and avoided the company of her husband. There are the Wickhams, where the husband had “cherished the hope of more effectually making his fortune by marriage in some other country” almost up to the altar. And there are the Hursts, where Louisa “had married a man of more fashion than fortune” who turned out to be a non-entity.
So Mr. Hurst’s role in the novel is to be a negative example. He is one kind of bad husband, to be contrasted with Mr. Darcy and so emphasize the good qualities of the latter.