Nishio sensei was a true master of atemi. Not only did he know so many ways of doing it, but he could do it so fast that our eyes couldn't see it. Sometimes several atemi in a row.
He got most of his atemi from his karatedo experience and his sword art knowledge.
I see atemi, the way it is used in aikido, mainly as a distraction strike. We do atemi to cause a reaction in uke, which we can use to complete the aikido technique. The reaction shakes uke out of balance, and therefore also out of stability.
So, atemi could very well be compared to the break-balance techniques in judo. In judo it is mostly done by pulling or pushing, which is not suitable for aikido since tori is not supposed to grab uke initially, nor to pull and push.
Instead, the aikido break-balance is atemi, where we sort of flash a threat in front of uke, and make use of uke's instinctual reaction to it.
That means uke has to notice the atemi - and believe in its power.
Just waving a hand in front of uke's face is not enough.