I can think of a few reasons why a one-night stand doesn't fit in even a "modernized" version of Much Ado. For a start, the plot of the play still turns on a character, Beatrice's cousin Hero, being falsely accused of promiscuity. The fallout from the accusation is swift and brutal: Her fiancé, Claudio, leaves her at the altar, telling her father, "Give not this rotten orange to your friend." Her father, in his turn, declares that he'd rather see her dead than "tainted" in this way. A furious Beatrice, one of the very few to stand by Hero, insists that Benedick challenge Claudio to a duel. After the truth has been discovered and a repentant Claudio reunited with Hero, she declares publicly, "And surely as I live, I am a maid" (that is, a virgin). This is clearly a society that values pre-marital purity, at least for women.
However one feels about such a society, given that the Hero-Claudio storyline is still intact, Beatrice and Benedick's affair makes little sense. Flashbacks in the film, in fact, signal that it was little more than a hookup, aided by copious amounts of alcohol. That is even more incongruous in a setting in which Hero's chastity still matters so much. Hero's father hints at one point that an already-engaged couple yielding to temptation wouldn't be such a grave offense. But a drunken one-night stand--that would have gone against everything that Beatrice had ever been taught.
It also goes against the bulk of what Shakespeare wrote about casual sex. As Anthony Eselen has pointed out, "For Shakespeare, chastity is as near to an absolute value as it is possible for a virtue to be." Considering Shakespeare's work against the backdrop of pagan and Renaissance poets, Eselen continues, "Nothing in Shakespeare corresponds to the reveling in sensuality that we find in these poets...and that is all the more remarkable given his earthiness and bawdy humor."
There are other problems with Beatrice and Benedick's tryst. In an Atlantic interview, Whedon explains that his interpretation is meant to be about "the vulnerability of two people who had opened themselves up to something, but were not ready for it, ran away from it, and then blamed each other." Regardless of his intentions, that's not how the scene comes across on the screen. It appears that only one person (Benedick) is doing the running away, leaving the other person (Beatrice) deeply wounded.
As a trigger for the invective that Beatrice and Benedick will hurl at each other later in the story, this imbalance doesn't work. Shakespeare's text does suggest that Beatrice has been hurt to some extent, but that she is primarily a "merry" and not a "melancholy" person; she's having fun exercising her wit at Benedick's expense. (Imagine that, from a pre-feminist writer like Shakespeare!) The fact that she hasn't been seriously wounded by Benedick makes it plausible that she could so easily fall in love with him later, and so willingly drop the rhetorical weapons she's been wielding against him.