The list of faulty of outright fraudulent experiments done in any number of fields, especially the biomedical sciences, also grows ever longer, but it it seems this argument is hardly ever leveled here. It's well-established now that these problems exist in other fields, such as immunology, oncology, and other fields. Even closely related fields, such as the neurosciences, have been shown to be full of improbable and unreplicable findings, and many neuroimaging results are not interpretable in the way that claims are made of them.
Theranos anyone?
Every field should be looked at with caution until the perverse incentives that currently exist in academics are addressed.
What I see instead is a bias in certain physical sciences to think that somehow experiential phenomena are less rigorous because they don't fit the mold of those sciences as much. The systems are more complex and different metaphysically, so their legitimacy is questioned. This is somehow still happening even as developments in fields like quantum physics and AI are leading many very competent scholars to question basic assumptions about the nature of experience and consciousness vis-a-vis physically observable phenomena.
The irony of the Rosenhan study is that Rosenhan was putting forth exactly the same arguments as you, that psychiatry lacks rigor because it's too subject to the whims of subjectivity. So when this paper is shown to have been a fraud (even though it was dismissed in the field for many other reasons, but overall because it was unscientific) it is evidence that psychology is unrigorous? When it is not widely known to be a fraud per se, it is cited as evidence that psychology is unrigorous as well? It seems there's no way to win: the critics of the field cite this work as evidence of lack of rigor, and then when it's shown to be fraudulent, it's also shown as lack of rigor.
The even greater irony is that many of these fraudulent studies are being identified by... you guessed it, psychologists. I would go so far as to say no field has done more for the scientific study of science than psychology. Meta-analysis has its birthplace in psychology, and all these discussions of replicability ultimately flow from psychology as a field. If anything, psychology is among the only ones to be open about these issues and to take them seriously. In many other fields, they're swept under the rug, and questioners are attacked with arrogant hostility and accusations of incompetence.