>>2917288Iirc it wasn't ABe, but Takahiro Kishida that pushed for it.
But there is some symbolism I think, real world Lain uses it to protect herself from everything.
Even going out with friends she wore this hat, so it's a comfort thing at the very least.
We never see wired Lain in it, and Lain's dad tells her she doesn't need it anymore at he very end.