I think it's pretty much because she was dead. And I mean dead dead, not just drowned briefly. She was a (icky) corpse. The First takes the form of vampires all the time. I realize that they're undead, but notice that the First looks like they do now, not before they were killed, which would make sense if it needed the soul to replicate or something (which would mean that looking like Buffy wouldn't make a lot of sense).
I don't think I'm saying this quite right. Here's an example: when the First is Drusilla, it's Drusilla as she is as a vampire, not as she was before she was turned. Drusilla the vampire is still walking around, but her soul is gone. Her soul is the dead part. If the First needed the dead person's soul to, like, photocopy, it wouldn't make sense for it to look like Drusilla-the-vampire because that's not how the soul would look. And if that were the case, since Buffy's soul was returned, the First wouldn't be able to look like her.
I think it's just a writer-imposed limitation to keep things from getting too confusing and giving the First an even bigger unfair advantage (like it not being corporeal).
And I think the First got off on the irony of looking like the Slayer when it was trying to wipe out the Slayer line.