Okay, the title is a bit misleading. This is more like an observation. I'm not really Kisuke, so I can't work out the technical stuff on how it works. I do have a fair idea, however. For some of you, this might be obvious. If so, read it anyway. =).
I don't think shinigami actually split from their zampakuto at any point. Obtaining shikai and bankai involved 2 different yet similar processes in principle. For shikai you have to go to your inner world where the zampakuto spirit inhabits and learn his name. For bankai the process is the opposite, rather than entering the inner world you call out to it to the real world. I don't think this would necessarily entail an actual split. Another thing, the doll simply accelerates the bankai training as it materializes the bankai however it has never actually been said or implied using the doll has any actual effect on the user or the resulting bankai.
If we consider ichigo's case then it seems even more likely there is no splitting going on. Remember when he trained for saigo no getsuga tensho? At that time he went into his inner world and zangetsu was there albeit with another form. Your theory would imply zangetsu shouldn't have to be in the inner world for bankai to work right?
What about Mayruri? Hopefully he will(has?) figure it out for us, plus they prob couldn't steal Mayuri's as he will highly sabotage it (= Mayuri vs Szayel)
Yeah, sounds like that's about it. I guess Quincy don't take the sword itself, but the spirit of the sword.
(Also, I think Kenpachi does have an actual "zanpakuto" but he doesn't know its name or any of its abilities.)
And yeah, I'm waiting for some hapless Quincy to "steal" Mayuri's Bankai, hahaha.
A lot of your post is based on power scaling which I won't get into because a) I can't be bothered and don't care enough b) it's too controversial c) it's at least partly conjectural and d) it assumes there's a consistency in the power levels. But I'm perfectly willing to admit that everything in your post regarding people's relative strengths is true. However, the following point still stands: Kido doesn't guarantess victory, obviously. And it's going to be less effective than going all-out with Bankai. Maybe Kido won't even do any damage at all to them, as you suppose. But it's got to have a better chance than what Byakuya actually elects to do: swinging his sword at them.
He'd already seen that normal sword swings will get shrugged off, but he tries it again anyway. He doesn't even attempt Kido, even as a supplementary manoevre. Even if it failed (and I agree, at the level the Quincies are at, it's probably going to), at least he could report "Don't bother trying Kido guys, it doesn't work."
The counter measure to the medallions, I imagine could be killing the user itself. Besides that, you'd have to be very powerful (as Kenpachi has already demonstrated) in order to fight the Star Knights without Bankai. However, I think it's kind of bullsh*t for Kubo to say that the Captains and some of these Star Knights are all on the same level of strength. I know, Byakuya could've defeated As Nodt without Bankai. Hell, he's mad skilled in kidou arts, what happened to that, Kubo?.
I don't think I got into the whole power scaling thing there. At least I don't think saying aizen is stronger than komamura or byakuya goes as far as being a power scaling discussion lol. I think in this case you underestimate the simple swinging of a sword though, at least considering what a zampakuto represents to a shinigami (their power, self, soul and whatnot). Other than against ichigo, hierro was at large useless against shinigami. It did not help nnoitora against kenpachi, it did not help zomari against byakuya, it did not protect stark from shunsui and it certainly did nothing for harribel. In general a zampakuto slash has shown to be quite powerful to say the least. That said, in byakuya's particular case he has not shown an exceptional amount of high level kido. He has shown 2 ranged hado as far as I recall, the level 4 one he used against ichigo and the level 30 something one that he used against renji and yami. As far as bakudo we have seen some higher level stuff (63 and 89 if I recall) but I doubt any of them would have been useful against nodt. Not to mention that the hado byakuya has shown are ranged attacks, I doubt it would be a smart move on his part to keep a ranged battle against a quincy with kido, he would at least need his shikai for that IMO. I mean, ranged battling is kinda a quincy's thing.
We could now see that getting your Bankai stolen doesn't mean your Zanpakuto Spirit is gone, since Byakuya could still use Shikai. But still, what the OP said about the difference between Bankai and Shikai holds some merit. Bankai is an outward manifestation of the Shinigami's Spirit in a combative form. The possible key might lie in the very definition here.
Shikai is a partial release. Bankai is a full release. I remember when Kirge could absorb Ayon, who was basically a manifestation of the Tres Bestia's power in a seperate form. I think these medallions are a tool utilizing a more specialized version of this technique. The ability to absord spirit particles and constructs of spirit particles. Since Shikai is not a full manifestation of a Shinigami's power, that might be the reason that it's physically impossible for Quincy to absorb/steal them. A Bankai is a full manifestation however, an that might make it technically possible. Ofcourse stealing someone's Bankai is the same as stealing their Reiatsu, it is a part of the Shinigami. That presumably makes it more difficult. But it may also have negative side effects to directly absorb a bankai power. Remember how Kirge looked as if he swallowed a barrel of uranium after he absorbed Ayon? That seemed like a serious drawback. So in order to facilitate bankai stealing ad avoid nasty side effects, they don't absorb it into themselves, but rather use specialized tools the seal them in. If this holds true, then these medallions work only on Bankai, not resurreccion.
How does it not affect Ichigo? Well there are two ways in which his Bankai differs from others we have seen so far. One is the compression of Reiatsu. Though if my theory about the workings of these medallions is correct, then I highly doubt this is the reason his bankai cannot be stolen. The other big difference is that he can actually combine with his Zanpakuto, and he has done this through the final getsuga. Plus it was hinted that his hollow and shinigami powers have fused, as was seen during his training. Point is, Ichigo's bankai seems to be more of a part of him than other bankai so far. That might be why it's impossible to just rip it away.
On a side note, this is indeed probably the reason why Ichigo is called a war potential. I think it simply means that he is a legitimate threat. He has the potential to beat the Sternritter due to his immunity to bankai theft. The Sternritter are captain level combatants. They are normally equal to the SS captains. However, the captains can only use Shikai against them, which give the SR a considerable advantage. Stealing Bankai means that the captain is not only limited to using Shikai, but must face a strong opponent who just gained their own secret weapon, their greatest power. That is pretty much overkill. However, these fail-safe ways of defeating Shinigami do not apply to Ichigo. Which makes him someone with the potential to turn the tides of battle.
Kenpachi is a captain level combatant using only his constant release type shikai, making him a huge threat. He has already made his epic appearance carrying two dead SR on his back. Most people agree he is one of the 5 war potentials. I think Vandenreich wants to attack SS when a maximum of 1 or 2 war potentials are present since they waite for Ichigo to be cut off from SS.
If Ichigo's bankai cannot be stolen due to FGT, if that holds true, then it's pretty much certain that Isshin, who is not a resident of SS, is also a war potential.
The fourth is obviously Aizen. For one, his Shikai is not funny to fight against. Not funny at all. Once the most annoying, hax ability in the manga, it'll be pure gold to see him WTFPWN Quincy ass. However, during his hogyoku transformations, he seemed to blend/combine with his Zanpakuto in a similair way to Ichigo before he went FGT. This might indicate that he is also more combined with his Zanpakuto as a whle, whcih might make it impossible for his Bankai to be stolen. But his Shikai is simply hax, so that more than qualifies him.
The fifth is a toss up between Yamamoto, Harribel and Grimmjow. Yama's Shikai is hax, but I figure he needs Bankai to beat the VR leader. Which poses a slight problem. Then there are Grimjow and Harribel. They are captain level combatants and their full power, Resurreccion, cannot be stolen. This could qualify them. But seeing Harribel defeated and locked away by Beardman, Grimmie might be the most logical choice here.
The war potentials hold the potential to defeat Sternritter because they either 1) lack/don't need a bankai but can still kick ass or 2) have an unstealable bankai. But this does not mean that each of them could defeat Buckbeard.
Maybe they can just break those cheap little medallions lol?
Kenpachi does have a zanpaktuo and it does have a name (imo) because Zangestu was asking Ichigo if he "could hear the screams of his (Zaraki's) sword" during their fight
Zaraki's zampakuto having a name is a given. All zampakuto have a name, zaraki simply does not know his.
Now, I am kinda confused on the current subject matter. Take a look at this particular page
Hitsugaya attempts to communicate with his sword but he apparently gets not answer. Then we have this page:
This page seems to imply that even after losing bankai shikai is still possible.
Now, how would shikai be possible if the first link I posted seems to suggest it is the spirit itself which is stolen? Why would hitsugaya be unable to talk to hyorinmaru if he is still capable of shikai? Or perhaps ripping bankai out of a shinigami does not actually rid the user of the spirit but merely cripples it kinda? If the spirit is stolen then why are quincy able to use stolen bankai? Communication with the spirit is important to the power of a zampakuto and so far it would seem like there is nothing inside the badges other than the bankai.... Perhaps the badges are kinda similar to zampakuto in that they have feelings and personality and simply steal a zampakuto's power?
This is what confused me about the whole "bankai stealing". If you can steal Bankai, then Shikai should be impossible to use as well. Eventhough, I didn't see, Byakuya try to use Shikai against As Nodt. If you can't release the full power of the zanpakuto, then the medium (Shikai) should be rendered useless as well.
Ichigo's Bankai must be incomplete period. That's the only theory I've come up with as to why, it can't be stolen in the first place. That's why, the other Bankais were stolen because they are completed. Other than that, I'm not sold on the "half human" theory, because Quincy's are humans themselves.