Many fields have theoretical frameworks which do not utilize the scientific method alongside ones which do. The fact they don't use it is considered a criticism of those frameworks, even if they measurably have results.
EG; Freud.
Psychodynamic therapy has high success rates, which can be empirically confirmed. But the theory is unscientific. Another is, for instance, Erikson development "theory" in social work, which is useful to understand and has its uses even if its not scientific.
I like to think of these kind of discrepancies as akin to Pre-Euclidian mysticism about the round nature of the earth.
"The earth is round."
"Why?"
"Because obviously that's a more pleasing shape for the earth to be, more perfect, more holistic. So that's what the universe made it, because the universe is alive and likes to be pretty. Here, Our theory is supported by us noting that there are lots of pretty things around, supporting our model.".
Non-scientific theories in academia always remind me of that kind of logic.
It's like, no, it's just there's unknown unknowns we haven't found out about yet and you're coming up with a bunch of bollocks rather than acknowledge it.
Freudian psychology is bunk. It's guesswork and not scientific.
But it produces results for reasons we don't yet understand.
In the round earth example, that'd be the natue of gravity and how it produces sphere shapes for large bodies of mass. Once we understood that, we understood why the earth was round, and understood that the "Because sentient pretty universe" wasn't a proper explanation. For freud, who knows.
Humanistic psychology is a good one to consider here.
Just because Rogers couldn't scientifically prove his ideas, doesn't mean they don't have merit and aren't useful, but that also doesn't mean his ideas will never be scientifically proven, especially as our biomedical understanding of neuropsychology expands. And crucially, what he WAS able to do is scientifically prove;
"My ideas do produce results, even if I can't prove its for the reasons I say they do.".
https://en.wikipedia.org/wiki/There_are_known_knownsI.E
"Julius Caesar didn't know that he didn't know anything about nuclear physics.", but show him a radioactive substance and its impact on others, and he'll quickly come up with a model to rationalize what he is seeing, even if its based on a bunch of unscientific nonsense.