>>2881170>>2881332(cont again)
...and keep in mind that the other EVA's work because Shinji and Asuka have a mother. I know you'll argue about this as well, but technically? There was never any mention of a soul split for them either. The entirety of Yui's soul and body was put inside EVA01. With Kyoko, she went insane after a contact experiment, after which she commits suicide alongside her doll daughter. These are the canonical facts. Keep in mind that Asuka is not shown to pilot until AFTER Kyoko dies.
Both of them have in common the fact that they are both mothers to the child in question, and it is placed some emphasis that without this maternal connection, they would have no ability to pilot. But Rei has no mother. There is no necessity for Rei to have a mother for her EVA to function.
Keep in mind that Rei is not a regular human being, she is a Seed of Life, mankind's de facto deity of creation. Kaworu is also another such being except for the Angels, and he is shown to be capable of controlling an EVA regardless "as long as the soul inside is out of the way". Why wouldn't this also fit Rei's list of capabilities? After all, Rei can also create the most powerful AT-fields and other supernatural feats.
That Rei's EVA work like Shinji or Asuka's is already out of the question. Whose souls are inside the MP-EVA's for instance?
Point here being, there's no requirement like the other children, soul and all. It only complicates things further.