If the body and intent behind the movements isn't done as if it was atemi, it simply will not work. All of these movements impact uke's structure, but only if nage performs them as atemi. Most of our transition movements hit to uke's core, even if it's just positioning *because* they are done as if they are strikes.
I suppose there are ways to describe atemi that take in so much that there isn't any way to say it but that doing it right is doing atemi. If one were to describe atemi as any hand movement done from center with full intent, then yes, a lot of what I do is atemi. But that is certainly not the conventional description.
It seems we do a different art, my friend. Maybe they are both Aikido, who knows. I don't know if you would ever be happy doing Aikido the way I do it. I know I wouldn't be happy doing it the way you describe.
Works for me.
If you or anyone want to say that I am not doing Aikido because I do not really use atemi per se, or not the way they define it, that's fine with me. I know a lot of interesting people who might disagree though. :-)