Uhh, no, those aren't the implications I hate about the name "BlackMoonWhiteSun." And you're actually wrong about it also being a title for the IchiRuki pairing. When Ichiruki Fans refer to the pairing, they talk about the Black Sun (Ichigo) and the White Moon (Rukia). The name "BlackMoonWhiteSun" is obviously mocking the meaning behind those titles. But aside from mocking the pairing itself, the title is also insulting the series Creator Tite Kubo. In the manga there is this poem, HiKu, Mantra, whatever, that talks about a White Moon helping a Black Sun, it is obvious to anyone paying attention that the White Moon refers to Rukia and the Black Sun is Ichigo. There is an actual story and Meaning behind the titles, and because Tite Kubo wrote Both manga and the Poem (As far as I know anyway) the titles are fact and canon. Meaning that "BlackMoonWhiteSun" not only goes against the Ichiruki Pairing, but Tite Kubo's vision and original plan itself.

Oh, I just love your question because I am SO prepared!!!

But first, how far in the anime are you exactly? Because I'm sure I'm about to spoil a few things. Anyway:

1. Who says they have to choose at all? Why can't Rukia arrange to be stationed in Karakura Town and continue on as it's official Soul Reaper? Even though she'd be in Karakura Town permanentally she'd still have to report back to Soul Society and check in every few months or so just for a progress report, she'd be able to see everyone then.

2. Rukia is actually only 15. Okay, a soul ages 1 year to every human's 10. Even though Rukia has lived a considerably hard 150 years of life and matured more than she needed to, she is still 15, and as such acts like a 15 year old, a very mature 15 year old grant you, but still a 15 yearold.

3. Gigai's don't seal away Spiritual Power! Even though Rukia will be in a Gigai she can still use her kido, the only reason she couldn't in the first season was because she was still to weak and recovering from giving Ichigo her powers. All of the Vizards are in Gigai's and they all have their Zanpakto's and Masks!

Pay attention to this next part.

4. Rukia's soul isn't attached to her Gigai, she doesn't have a spirit chain that connects her Soul to her Gigai. This means that her natural Aging process won't be effected by the Gigai. The Gigai may age and wear out over time but Rukia's Soul will only continue to age every ten years, making it so that even though Rukia's "Body" may look about 40 years old, Rukia will be able to pop out of her body and only look about 17.

5. The same logic for Rukia applies for Ichigo. You see, when Urahara cut Ichigo's soul chain, he severed the connection between Ichigo's Soul and his Body. Ichigo IS still alive of course, but without the Spirit Chain, his Soul now ages like Rukia's while his body continues to age normaly. When Ichigo dies, it actually won't be anything more than his body simply giving out and not being able to support his spirit anymore. While his body is, let's say mid 60's and for some reason dies, his spirit will actually only look in his early 20's.

6. Reason Number 5. Now brings me to the other option Ichigo and Rukia have, this of course is a very extreme measure but still do able. Ichigo and Rukia could agree to wait for each other. This option is actually quite common in Ichiruki fanfics. This usually involves Rukia wanting Ichigo to live out a normal life and not want to burden him with her presence, even though it would be scientifically and physically impossible to do so. Ichigo of course refuses to let Rukia leave his life, so they make a comprimise that they will live out their lives in their own worlds, and promise not to get married or have anykind of relationship what so ever with another person. Then, because both souls now age at the same rate, when Ichigo eventually dies, they will both appear to be in either their late teens to their early 20's at most. They can then restart their lives happily ever after from that point on.

7. Reason 7. helps make Reason 6. even more plausable. First, Ichigo is NOT and I repeat NOT a playboy of anykind. Isshin LOVED Masaki obviously, and will clearly NEVER get over her or EVER date another woman. Because of like Father like Son, Ichigo will fall in love with ONE and ONLY ONE woman and will want absolutely nothing less. Second, Rukia will easily be able to keep up her end of the promise becase Byakuya cannot force an arranged marriage on Rukia because if he did he would be a giant hypocrite because of Hisana. Renji also isn't a problem because if you paid attention to his battle with Ichigo in the soul society, you would remember that Renji blew his chance with Rukia when he all but threw her at the Kuchiki family, thus Rukia has NO feelings for Renji that arent brother sister like.

8. Ichigo, Karin, and Isshin ALL see spirits. Hell Isshin is an ex-soul reaper. Yuzu is what we like to call a LATE BLOOMER, Yuzu will be able to see spirits eventually it will just take time. But that doesn't change the fact that Soul Reapers take off duty vacations to the Human world all the time, even though it's not specifically stated, it's obvious they'd be able to. If Ichigo moved to the Soul Society, it would be the exact equivilant to Ichigo joining the Army and moving to a military base.

9. And finally, Rukia is an artificial Daughter to Isshin and Sister to both Karin and Yuzu. There is simply no way Rukia would ever let Karin or Yuzu be alone. Rukia would NEVER let Ichigo forget his Family, and that's of course an extreme impossibility, because there isn't a single chance in hell that Ichigo would EVER forget his family.