Before I start, I should point out that I will be using the terms "Brilliant Starseed" shortened to "starseed" and "Sailor Crystal" interchangably. Frankly, if you're going to yank my chain about it, then you aren't really concentrating on the things that Sailormoon is really about.
Okay, this one is a big deal. In fact, it's one of the biggest splits I have with a lot of people in the fan community concerning the fate and true nature of Sailor Chibimoon. It's kind of a sticky issue, especially since I honestly believe that Naoko changed her mind about it while working through the series. Because her ideas about Chibimoon changed, Chibimoon's nature changed. Fortunately, in terms of story, we can write this off as the evolution of a starseed. Also keep in mind that for the balance of this argument we will be using the manga as the source reference simply because it goes into this stuff in far greater detail.
So what am I talking about, really? One of the easiest ways to put it is this "Will Chibimoon ever henshin into Sailor Moon?" My answer to this is a resounding "No." No matter how old Chibiusa may get, I don't think she'll ever henshin into Sailor Moon. She will remain Chibimoon because that has become who she is.
Okay, let's define a few things before we start out. The Cauldron Guardian tells Sailor Moon that all starseeds are born from the Galactic center. Thus, the potential for all Sailor Senshi is born right there. Mark that, I said potential. Little screaming senshi babies aren't spun off of the nexus of the Cauldron, the Cauldron simply spins off energy that coalesces into starseeds that may eventually produce Sailor Senshi. Why do I say may? Because everyone who is granted a brilliant starseed doesn't necessarily ever have to henshin into a soldier. Take Princess Serenity for example. She clearly had the potential to become Sailor Moon and yet she never did. Just because you can henshin doesn't mean that you will.
When Chibiusa first appears from the future in the second story arc, I think that Naoko intended her to carry on the Sailor Moon dynasty in the future. However, over the course of the story Chibiusa evolved into a strong and dynamic character (and one of Naoko's favorites). Because of the turns that the Sailormoon story takes later on, it becomes almost impossible for Chibiusa to become Sailor Moon because she is clearly her own person and not simply another reincarnation of Serenity. From the presence of Sailor Cosmos and Sailor Chibichibi, it's clear that Serenity will reincarnate even into the distant future. Presumably she will continue to be Sailor Moon and still call upon the ginzuishou (since it is another manifestation of her brilliant starseed), just attaining higher and higher forms of it (and eventually becoming Sailor Cosmos). We can also assume that the other senshi will also reincarnate in a similar fashion because Sailor Cosmos refers to losing all her friends in the future. Who else could these friends be other than her eternally loyal court?
If this is so and we assume that Chibiusa will eventually become Sailor Moon then unlike the other senshi, Chibiusa will never reincarnate. That means that this one shot at life is all she gets and that Usagi will never again meet her daughter in future incarnations. Well, that kind of sucks and I don't believe that Naoko would willingly do that to one of her favorites.
And she doesn't. Just trust me on this one. If you will recall, all through the second and third major story arcs of Sailormoon and even into the fourth one, Chibiusa uses the power of the ginzuishou of the future. This was established in the second arc of Sailormoon before Naoko had decided about all this eternal and reincarnation jazz. Chibiusa carries the ginzuishou because she's the one who's supposed to carry on the name of Sailor Moon in the future. She uses the ginzuishou. That's the manifestation of her shiny starseed, and yes, it is the same as Sailor Moon's, only it comes from the future. This would surely lead everyone to believe that Chibimoon is the Sailor Moon of the future. Their starseeds even resonate the same.
However, just about the time Naoko starts seriously thinking about having everyone reincarnate who knows how many bazillion times, Chibiusa goes through a transformation and her ginzuishou becomes the Pink Moon Crystal -- her very own brilliant and unique starseed. She is no longer using the ginzuishou. She is unique in her own right and no longer destined to be lost as the generations of senshi roll on. Because she is unique there's no real way she can now take the name of Sailor Moon. She has hewn out an eternal place for herself -- Sailor Chibimoon. The Galactic Cauldron may be the place where starseeds are born, but senshi, soldiers, are born from the heart. Chibiusa's heart and soul were strong enough to carve out a unique niche for herself.
As if to further differentiate Chibimoon as her own senshi, Naoko also gave Chibimoon her very own senshi team further sealing the idea that Chibimoon is not the future Sailor Moon. Chibimoon doesn't have a Lunar court, she has an Asteroid court who, when they first appear tell her that they'll come to her when she's truly awakened as a soldier in her own right. When she does so, and honestly is no longer a little girl or a small lady, they do appear to her and pronounce her a full senshi and she still identifies herself as Sailor Chibimoon.
Frankly, in my opinion if the crossover to Sailor Moon or even something else like Sailor Neo Moon was ever going to happen, then it would have happened there when Chibimoon joins with her senshi.
So there you have my case for it. Chibimoon does indeed have her own unique and brilliant starseed and it is exactly because of this that she will never become Sailor Moon. She isn't anyone's next generation. She is Sailor Chibimoon, soldier of the future moon, and that really should be enough for anyone.