Sure Giffin and DeMatteis didn't get a chance to explore the character much but with what we got it begs the question...was the character needed at all?
I certainly have trouble seeing why she was added to the mix. At first she was just a innocent kid stuck in an awful situation. Rani saw horrible things no one should witness much less a child. If she had no destiny surely Rip would have showed more interest in her. If she didn't turn up then a lot of the Giffin and DeMatteis run on the book couldn't have happened since her disappearance led to Booster going back to War World 2 which later led to a time paradox being created via an evil Booster. In fact that should be proof that her presence made things worse since Rips' explanation for said paradox doesn't really make sense in the first place. His mere existence proves the other Booster shouldn't exist or isn't our Booster.
We'll forget about the detail of someone looking for Rani in the 31st century but who could she be? Throughout the run everyone seems to be pushing Booster into becoming her father but she's not seen or mentioned in Time Masters Vanishing Point. I think Jurgens was keeping track of what was going on in the Booster Gold series and she gets acknowledged in the time lab in present day when he returns. The most logical answer would be Michelles' adopted daughter as she's the one that demanded Rani stay. Yet Michelle doesn't seem to be watching her enough to keep her from stealing the Goldstar uniform or using the time travel devices. The only responsibility Michelle takes is punishing Rani for the former incident since Michelle's advice almost got them killed. She's mostly seen pampering the girl and screeching at her brother about her in a very out of character way.
So Rani does affect Michelle but not in a positive manner and one with no real build up. We don't know why Michelle wants to keep Rani other than her being a "poor thing." She doesn't act like a parent despite Boosters' claims and doesn't share any real deep moments with her outside the one time she has to use the Goldstar suit to protect the time lab.
The relationship with Booster is forced in certain places like him proclaiming she made him believe in god where there's no scene to back that up with. Much less his suppose disbelief of god. They share the best moments together and seem the closest. That's kind of weird considering that Rani likely spent more time with Michelle and Rip in the Time Lab than him. It makes sense that she'd feel connected to him because of their shared traumatic experience but doesn't feel quite earned since he's always away.
Then there's the comparisons to Rip and this is where I have to wonder just what their plans were. It's revealed that Rani is a tech wonder that's apparently so advance she can understand time travel despite it being very hard to master (the Time Stealers despite their genius still struggled.) She even points out that Rip's off in a calculation and gleefully rubs it in. If she's supposed to be Boosters' adopted kid then I have to ask what's the point? Rip's the freaking TIME MASTER that we know has to be born to save all of creation. Now another genius kid comes into the picture and you have to wonder why is one really needed when you have the other?
The name Rani means Queen and sometimes Princess. In time travel circles I recently learned there's another link. (I haven't watched Dr. Who.) So with that in mind one has to ask if she was destined for a much darker path. This is a kid that watched the Emerald Empress slaughter other passengers. Would that trauma and all the time travel be too much for her leading to Rani becoming a super villain?
Overall I didn't see much need for the character especially after they changed Michelle's personality and made Rani a mini-Rip-in-training. I enjoyed some of the ideas she brought like Booster exploring what fatherhood meant to him but other than that she just seemed to get into trouble. Still it would have been nice to see where this was headed with another writer.