In the classic Georgette Heyer Regencies (to which authors like Wrede and Stevermere and Bujold all owe a debt), it's not uncommon to have either the hero or the heroine interested in marrying for money, whether they're thinking mainly of their own future, or needing to place the welfare of their impoverished family above their own desires. It's not like Heyer protagonists are all crazy mercenary, and certainly, romance, love, and happiness are valued above money or status in almost every single one of her many books (I believe there is exactly one where someone marries a woman he doesn't love for her money; although the story ends on a positive note, it's generally acknowledged to be both darker and much less of a romantic fantasy than most of her books), but Heyer is smart enough to acknowledge that financial stability is not a trivial thing, and that is an important aspect of future happiness--even in fantasy, money still shows up.

Obviously, even if your romantic protagonist is interested in money, he or she has to end up in love, whether or not the love is accompanied by money--romances are about finding love, after all--but yeah, in the Regency romance, wanting to marry wealth isn't something that a character needs to be punished for, or to stop wanting; it's a normal, acceptable desire.