So (the goal of) aikido is the coordination of body and mind?
It most certainly is. It is such a powerful way to train that entire arts have been named after the idea in China.
I think it is worth considering that Shihan with decades of experience think this method of training is the single most powerful tool they have ever encountered. Two of your senior teachers have told me they would trade every technique and past approach in their entire career ....for this.
Of course my response is "Why not have both?"
If I achieve this through training in e.g. singing, then I'm performing aikido?
No, you're not. You might become a better singer though.
I agree that mind/body is not all of it, so I see your point. The trouble in communication arises when people cannot see that it is thee, single most, powerful aspect of Aikido. That it drives everything else. Have you ever wondered why the aiki arts, had such unusual approaches to movement? They were designed to be driven by aiki power. Without it, all you really have is a jujutsu system, and not a very good one at that. I think getting your hands on some people who have it is a good start, then getting your hands on people who really know what to do WITH IT in motion, might help to define things more clearly.
If people do not understand the idea of mind/body connection and the power it trains in their body, then they simply do not have aiki. It is that simple. I continue to sit at tables with teachers who have trained with Kisshomaru, Arikawa, Yamaguchi, Chiba, Yamada, Kannai, Tohei, Saotome, Satio, , on to DR's Kiyama, Okomoto, Kondo, etc., who all....to a man, say this is the most powerful training tool they have ever felt.... At this point I don't think that opinion is going to change much. Mind/ body connection is king in the martial arts.
Good luck in your training