But speculation is fun.
Neo is the personification of "The Anomaly".
Smith is the multiple personification(s) of The Anti-Anomaly.
But when Neo gets to The Architect, he is shown all sorts of versions of himself.
Why couldn't Neo be multiple persons? He already is,
within the matrix. Or The Architect is lying !
Maybe the script writers thought, that would be too complicated for the viewers to handle.
So they wrote him
as if he was one dude, even though he wasn't.
And in any case ... why would The Anomaly absolutely have to coalesce into one personification?
Spooky ... there's something wrong with The Anomaly ?!
... but not the matrix
So maybe what would have happened if Neo took both pills,
is he would split into two halves, and just for the convenience of the writers and the pills and the audience.
hmm ... only conclusion I can draw is: He can't be John ...