Now I’m getting in the weeds and questioning the motivations of party A. I suspect this might make party A feel the way party C does when people call them “useful idiots”. And perhaps it demonstrates how this line of questioning is an endless rabbit hole.
I think the criteria "that party B calls party C" is actually pretty irrelevant to the concept's usefulness.
> essentially an argument meant to invalidate popular support for party B
In most of the cases where I'd use the term "useful idiot" the "party B" doesn't have much popular support, but is rather engaging in manipulation, disinformation, dishonest propaganda, etc. The realization isn't useful as a dismissal, but rather as a reminder that you need to confront both the idiot's sincere belief along with their ignorance of it's goals, implications, and beneficiaries.
It's not necessarily relevant to this case, and I agree that calling those people out as such lowers the quality of discourse, but I think it's something important to keep in mind.
[1] https://en.wikipedia.org/wiki/Useful_idiot