>> Fwiw, the Big 5 (OCEAN) personality inventory is one of the more robust findings in psychology (much more so than all the examples from the blog post)

That depends on who you ask:

Many investigations into the structure of individual differences theorize in terms of latent
variables, but rely on Principal Components Analyses (PCA) when it comes to the analysis of
empirical data. However, the extraction of a principal components structure, by itself, will not
ordinarily shed much light on the correspondence with a putative latent variable structure. The
reason is that PCA is not a latent variablemodel but a data reduction technique (e.g., Bartholomew,
2004). This is no problem as long as one does not go beyond the obvious interpretation of a principal
component, which is that it is a conveniently weighted sumscore. Unfortunately, however,
this is not the preferred interpretation among the enthusiastic users of principal components
analysis.

Consider, for instance, the personality literature,where people have discovered that executing
a PCA of large numbers of personality subtest scores, and selecting components by the usual
selection criteria, often returns five principal components. What is the interpretation of these
components? They are “biologically based psychological tendencies,” and as such are endowed
with causal forces (McCrae et al., 2000, p. 173). This interpretation cannot be justified solely on
the basis of a PCA, if only because PCA is a formative model and not a reflective one (Bollen
& Lennox, 1991; Borsboom, Mellenbergh, & Van Heerden, 2003). As such, it conceptualizes
constructs as causally determined by the observations, rather than the other way around (Edwards
& Bagozzi, 2000). In the case of PCA, the causal relation is moreover rather uninteresting;
principal component scores are “caused” by their indicators inmuch the same way that sumscores
are “caused” by item scores. Clearly, there is no conceivable way in which the Big Five could
cause subtest scores on personality tests (or anything else, for that matter), unless they were in
fact not principal components, but belonged to a more interesting species of theoretical entities;
for instance, latent variables. Testing the hypothesis that the personality traits in question are
causal determinants of personality test scores thus, at a minimum, requires the specification
of a reflective latent variable model (Edwards & Bagozzi, 2000). A good example would be a
Confirmatory Factor Analysis (CFA) model.

Now it turns out that, with respect to the Big Five, CFA gives Big Problems. For instance,
McCrae, Zonderman, Costa, Bond, & Paunonen (1996) found that a five factor model is not
supported by the data, even though the tests involved in the analysis were specifically designed
on the basis of the PCA solution. What does one conclude from this? Well, obviously, because
the Big Five exist, but CFA cannot find them, CFA is wrong. “In actual analyses of personality
data [. . .] structures that are known to be reliable [from principal components analyses] showed
poor fits when evaluated by CFA techniques. We believe this points to serious problems with
CFA itself when used to examine personality structure” (McCrae et al., 1996, p. 563).

Denny Borsboom, The attack of the psychometricians, Psychometrika. 2006 Sep;71(3):425-440

https://pubmed.ncbi.nlm.nih.gov/19946599/

In other words: bad statistics, badly applied.