The point is not that you can't cut みません into み and ません. The point is that it should be one single gap in the first place.

It's like cutting gaps out of English sentence like this: I'm [go][ing] to beat the shit out of that guy. Sure we know the logical way to break down 'going' is 'go' and '-ing', but it should be one single gap anyway.

Damn, where did that example come from? :P