If Dax had become male, that scene where Ezri and Worf were stranded on a planet after she went looking for him and they wind up in each other's arms might have been played quite differently.
They probably could have used a third female character from the beginning, but the problem would have been where to put her. Odo? Then both main Bajoran contacts would have been female. A female Quark wouldn't work if females weren't allowed to participate in business. A female Starfleet doctor would have been a repeat of Beverly. O'Brien was there to pull TNG fans. That leaves Sisko, and TPTB weren't ready for a female leader yet.