Obito staying in Kakashi is limited by time though, even the
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that he can stay in that world; Obito is no different. The fact that Kakashi's powers are
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will ultimately be his downfall in this match.
If Kakashi is in the ice he will be stuck immediately, and from my knowledge an intangible object can not touch a tangible object. So this leads Kakashi back to using Kamui to come out of the ice, Kagaya can easily use dimension shift to remove herself from the ice.
Now if Kakashi charges at her with kamui raikiri attempting to avoid being trapped in ice, Kagaya can easily avoid it by
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, which ultimately leads to Kakashi wasting his powers/wasting time.
Kagaya can use
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, which Kakashi has no counter or check. Furthermore
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would drain Kakashi's chakra out, leading to him becoming basic Kakashi without kamui, PS, rikudou chakra. And yes, Kagaya has the jutsu since BZ
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that zetsu were created by the first IT and IT alone doesn't turn people into zetsu.