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After delving into this again, and seeing the evidence from both sides, I find myself agreeing with the OP's conclusions. And my reasoning for this is contingent on understanding how the Cycle of Transmigration functions.
We know that Quincies mess with the Cycle of Transmigration by erasing Hollows from it, which causes imbalances that threaten the very cosmology of the verse. It's affecting it by specifically erasing the Souls of these Hollows - consequently resulting in them not being able to participate in the cycle anymore as they lack the necessary substance to do so.
If we have this prior knowledge of the act of erasing a Soul is what causes them to be unable to Reincarnate again, it logically follows that what Ichibe is doing is something similar to this - merely erasing someones' totality, which results in them losing substance within reality, and then results in them being unable to undergo Rebirth.

The main purpose of this forum is to discuss how to properly index the statistics of characters from a wide variety of different fictional franchises.