I understand where people who want Jenny to have been "real" are coming from; I think it was bound to be disappointing to get the usual instant-child sci-fi cliche. However, I don't think having her be a pre-existing daughter would have worked within the context of this story. Aside from the narrative problem that you would have to get into Time Lord-y backstory and "how did she survive the Time War" and "why didn't the Doctor sense her"-- in other words, stuff that would have made this episode into even more of a series three finale retread than it already was, and broken the story-element camel's back-- that would soften one of the themes of the episode, and indeed of the new series as a whole.
At first the Doctor rejects Jenny for the same reason some fans are-- she doesn't count because she's not properly his daughter. He does this not because it's a well worked out scientific argument, but (as he tells Donna) because he's emotionally burnt out from losing his family in the Time War and doesn't want to take the risk of connecting with her. In other words, he's making excuses to avoid a real commitment, just like he does whenever a companion pushes him to relate to people. The excuse fails because he's presented with evidence that she is already connected to him. Like in the moment when he's listening to her hearts beating and having that "Oh dear god you came from me" moment that parents who aren't in Instant-Child-Just-Add-Plot-Device scenarios have with newborns. If the story had been about Susan's mother or whoever he wouldn't have had the same grounds to reject her, and you'd lose his accepting this new relationship just in time to have it torn away from him. You could still try to hit the same story beats, but I don't think they would have the same impact without Jenny's unorthodox origin. Plus, of course, her being a product of the machine unifies the themes of militarism and the "endless" war in a way that they wouldn't be if it was just Romana Jr. participating in a local conflict for reasons of her own. Again, there's still story potential there, and you get to the same themes in a new way, but I think that at some point one has to judge the episode on its own merits rather than asking why it isn't something completely different with the same title.
At first the Doctor rejects Jenny for the same reason some fans are-- she doesn't count because she's not properly his daughter. He does this not because it's a well worked out scientific argument, but (as he tells Donna) because he's emotionally burnt out from losing his family in the Time War and doesn't want to take the risk of connecting with her. In other words, he's making excuses to avoid a real commitment, just like he does whenever a companion pushes him to relate to people. The excuse fails because he's presented with evidence that she is already connected to him. Like in the moment when he's listening to her hearts beating and having that "Oh dear god you came from me" moment that parents who aren't in Instant-Child-Just-Add-Plot-Device scenarios have with newborns. If the story had been about Susan's mother or whoever he wouldn't have had the same grounds to reject her, and you'd lose his accepting this new relationship just in time to have it torn away from him. You could still try to hit the same story beats, but I don't think they would have the same impact without Jenny's unorthodox origin. Plus, of course, her being a product of the machine unifies the themes of militarism and the "endless" war in a way that they wouldn't be if it was just Romana Jr. participating in a local conflict for reasons of her own. Again, there's still story potential there, and you get to the same themes in a new way, but I think that at some point one has to judge the episode on its own merits rather than asking why it isn't something completely different with the same title.