When the "something missing" argument is wielded in a debate about research, two consequences usually seem to be implied:
1. That psychotherapy research cannot tell you very much about what psychotherapy is really like, and so should not be trusted in appraising whether it is helpful.
2. That psychotherapy research does a sort of crass violence to the psychotherapy relationship itself, and that psychotherapy researchers are naive to think they can capture something so delicate.
The "something's missing" argument is often stated as though it were a knock-out blow to the value of outcomes research. It isn't. That something should be left out whenever we attempt to measure or represent something else is a banal truism. It simply presents no problem to the project of learning about reality. I am sure I have quoted Paul Meehl on this question before. In his book on statistical prediction, he refutes those who claim that any aspect of human behaviour is too complex to be in principle predictable from regression models, because humans are "more than" the models in question:
"A cannon ball falling through the air is “more than” the equation S=½g, but this has not prevented the development of a rather satisfactory science of mechanics".
The same goes for all of science (the full reality of a Large Hadron collider is more than the sum of the research produced by the physicists who work with it, but the research they produce does not lack veracity or utility in virtue of that fact) and the humanities too (no quantity of historical books on the American Civil War will ever completely reconstruct the experience of someone who fought in it). In fact, it is inherent to representing a state of affairs in any form other than the original.
So yes, psychotherapy research has "something missing", but that is trivial and we have to either accept the limitation or offer solutions to it (which is to say, become methodologists rather than critics). The choice we have is not between trite, uninformative quantitative research and rich-full-blooded qualitative information, it is between some combination of those two approaches and sheer guesswork.
Quantitative research does not just forget the magic of the interpersonal encounter, it factors it out in a bid to discover a separate numerical truth: how many people show some sort of measurable improvement (and how much of one)? This can look clumsy, but it is actually necessarily revealing to escape the persuasion of interpersonal charm and the therapeutic relationship. Think of a doctor like John Bodkins Adams, who appears to have been very successful interpersonally. He was sufficiently charming that he received money from many of his patients in their wills and became a extremely successful GP. Only something as crass as a body-count (Bodkin-Adams may have killed as many as 160 of his patients) revealed that something untoward was going on.
We should think of psychotherapy outcome research as analogous to the body count. Without it, we are too apt to be misled by the charisma and good intentions of the therapy industry.