We don't know that if the fight continued, it wouldn't go something like this: Alucard goes for the killing blow, Trevor dodges, whips Al upside the head and gets, at the very least, a K.O. victory.
Alucard destined to defeat Dracula sounds like a human story, not a real prophecy.
The Belmonts were feared for their power at this point, so who would write that they were destined to defeat Dracula?
The Vampire Killer, at the point of CV3, didn't even have a name, let alone being singled out as THE vampire hunting tool. As far as anyone knew, and I think it'd be better this way, the whip was just a weapon passed on from generation to generation of skilled vampire hunters, who knew various ways to kill a vampire.
I think the whole, no whip, no vampire hunting for a whole vampire hunting lineage sounds ludicrous.