If I had to pick a core point of disagreement, it would be something like:
I believe that if you have a bunch of different variables that are correlated with each other, then those correlations are probably because they share causes. And it is coherent to form a new variable by adding together these shared causes, and to claim that this new variable is an underlying factor which influences the bunch of different variables, especially when the shared causes influence the variables in a sufficiently uniform way. Further, to a good approximation, this synthetic aggregate variable can be measured simply by taking an average of the original bunch of correlated variables, because that makes their shared variance add up and their unique variances cancel out. This holds even if one cannot meaningfully intervene on any of this.
I have varying levels of confidence in the above, depending on the exact context, set of variables, deductions one wants to make on the basis of common cause, etc., but it seems to me like your post is overall arguing against this sentiment while I would tend to argue in favor of this sentiment.