I say we keep the "p-factor" idea. Since it seems to identify a pattern, maybe it will turn out to be useful.
How often has science/mathematics found the existence of certain figures and factors that turn out to be useful in predicting outcomes? Look at irrational numbers and constants. They allow us to create formulas and predict findings that we wouldn't be able to without these hypotheticals.
We can't write out the number which is the square root of 2 or PI, but we can use these numbers to solve certain mathematical problems by squaring them or inserting them in equations, e.g..
We will certainly discover biomarkers in mental illness, but until then, let's use the tools we have and that which is newly discovered...and figure out much later why they actually worked.
Maybe the P Factor will turn out to be the Higgs Boson of psychiatry.
Good article!