I only know what you have told me. You have told me that anything done with aiki can be properly called aikido. If I accept that statement as true, it logically follows (since aiki is not exclusive to our particular martial art), that many different martial arts and activities could be accurately and properly called aikido, at least some of the time. And if that is the case, then the term aikido cannot function as the name for our particular martial art.
Even if I don't understand you at all, even if I don't understand aikido at all, that's still how language works.
As I've said from the beginning, I think that your definition is much too narrow. You're defining it along the lines of what you're doing in your particular dojo - which is fine, but other dojo still calling themselves "Aikido" are doing completely different things, right down to the technical curriculum.
I could say that I practice "dance", or even "jazz dance", and everybody understands my language quite well, but in practice that covers a huge range of activities. That's how language works.
Anyway, that's pretty much all that I have to say about that.