I prefer to take a pedantic view of atemi as a "hit (to the) body"... and that such "hits" will result in one or more of the following:
1. A predictable physiological response in uke
2. Disturb/disrupt or even break uke's balance
3. Causes uke to change their priorities and respond in a predictable fashion
4. Create an opening to allow insertion for a technique
5. Allow for completion of the technique
I agree. Very well put. That's how I try to use atemi.
Regardless of the video and book discussed above, it was my experience that Nishio sensei used atemi in this way, too.
Primarily, he used atemi to show the attacker that attacking is wrong, thereby giving the attacker a chance to cease with it. A kind of philosophical statement, which Nishio sensei had at the entrance to every technique, taking a superior position and showing it to uke with an atemi - sort of saying: "See what I could do to you."
It is particularly evident in his sword techniques.
Secondarily, he used atemi in the ways described in 1-5 above.
Nishio sensei also insisted that aikido students need to know about proper atemi, so that the atemi become believable and functional. Otherwise they would not work as deterrents, nor that well in the 1-5 functions above.
So, when he showed how to strike, it was not to teach students an alternative to aikido techniques, but a functioning atemi deterrent/distraction/et cetera, to use with the aikido techniques.