Being a guy, I can only guess that the song's appeal to its many female fans lay in its unabashed embrace of feminine archetypes. Critics dismissed the aggressive, cathartic tone of the song and its parent album Blurring the Edges as being inferior to the music of a certain other angry female singer.
"What Would Happen" positively smokes with sensuality. There's no dirty language; no mid-coital moaning; nothing more explicit than a french kiss, and yet the song is hotter than any other I've ever heard. Sure, it's about nothing but an imagined tryst, but damn if you can't feel the lust, the yearning in every word. One of Brooks' greatest strengths was her smoky, tantalising voice, and this song plays to that strength perfectly.
(The music video bears a similar erotic intensity, but it's marred by laughable fetishism and the presence of Severus Snape.)