What are some criticisms of HEXACO from the Big Five camp? I read the 2009 review-ish chapter of McCrae in The Cambridge Handbook of Personality Psychology and I noticed he never once mentions HEXACO (or its 6th axis: honesty-humility), although McCrae does spend the spacetime to debunk a (totally obscure to me) Polish model of personality that had added a 6th spirituality factor. That to me felt like sweeping HEXACO under the rug, so to speak.

Most of the research on relating HEXACO to Big Five has come (unsurprisingly) from the researchers/proponents of the former, see e.g. What are the correlations between HEXACO and NEO-PI factors? 

So, has there been some explicit criticism of HEXACO from the Big Five "heavyweights" (well known researchers/promoters)?



There is a passage in the same book in another chapter by Boele De Raad noting that: 


  While the Big Five structure has found large adherence, claims for psycholexically
  based factors beyond the Big Five have been made, for two reasons mainly.
  The first reason is that the correlation matrices may not be optimally exhausted,
  and the second reason is that the trait domain may not be truly exhausted. This
  second reason comes in two versions, one suggesting that the psycholexical
  approach has been too restrictive in selecting personality descriptors (Almagor,
  Tellegen andWaller 1995), and the other suggesting that the psycholexical approach
  has been restricted to the use of trait-descriptive adjectives (cf., De Raad and
  Hofstee 1993).
  
  Ashton and Lee (2001) argued along the lines of exhausting the correlation matrix.
  They suggested that an additional Honesty-Humility factor, representing such
  traits as honest, sincere, fair and just, versus dishonest, conceited and boasting,
  could systematically be extracted. Support for this sixth factor was observed in
  several languages (Ashton, Lee, Perugini et al. 2004), but not, or not clearly, in all
  languages where this sixth factor was studied, as in American-English (Ashton,
  Lee and Goldberg 2004), Turkish (Somer and Goldberg 1999) and Croatian
  (Mlacic and Ostendorf 2005).


This is basically lexical criticism, but since the lexical perspective was hardly dominant in the development of the Big Five (according to the highly cited review of McCrae and John, 1992), this lexical criticism seems like a rather minor point.

Also note that De Raad himself appears to favor lexicalism, having proposed an eight-factor model from the latter perspective, by extending analysis to more parts of speech than the traditional approach using just adjectives. So De Raad's criticism of HEXACO being from a lexical perspective isn't surprising.
We had a discussion of the pros and cons of the HEXACO model in a recent article that draws on arguments and evidence presented by the &quot;heavyweights&quot; of the Big 5 (Anglim, &amp; O'Connor, 2019).
Here is the quote of the paragraph that focusses specifically on the critiques:

Although the HEXACO model is receiving growing support, the necessity
of a sixth broad trait, as well as the nature of this trait are
subjects of current debate.

First, other prominent six factor
inventories including the Hogan Personality Inventory (Hogan &amp; Hogan,
1992), the Six Factor Personality Questionnaire (Jackson, Paunonen, &amp;
Tremblay, 2000), and Saucier's Big Six (Saucier, 2009) have not
converged on the same sixth factor in the same way that has broadly
occurred with the Big Five (De Raad, Barelds, Mlačić, et al., 2010).
Second, while several lexical studies have broadly supported the
HEXACO model, the support is far from universal.
Third, Saucier and
Ostendorf (1999) have argued that any broad trait in addition to the
Big Five will correlate highly with one of the existing Big Five, and
honesty-humility correlates relatively highly with agreeableness (r =
.67 in Gaughan, Miller, &amp; Lynam, 2012). Honesty-humility also
correlates reasonably well with straightforwardness and modesty facets
of agreeableness in the NEO-PI-R, suggesting that a comprehensive
facet-level model using the Big Five may provide similar predictive
benefits (Costa &amp; McCrae, 1995; Gaughan et al., 2012).
Fourth,
Barford, Zhao, and Smillie (2015) mapped the Big Five and HEXACO
traits to a common space provided by the interpersonal circumplex, and
found that honesty-humility occupied a fairly similar space to the
politeness aspect of B5 agreeableness.
Finally, Condon (2017) assessed
the covariance structure of approximately 700 statement-based
personality test items drawn from the most commonly used public-domain
personality measures (including an approximately equal representation
of items from prominent five and six-factor measures). While he found
support for a large number of narrow traits, factor analysis suggested
five broad traits, and when six factors were extracted, the sixth
factor did not correspond to honesty-humility.


References:

Anglim, J., &amp; O'Connor, P. (2019). Measurement and Research Using the Big Five, HEXACO, and Narrow Traits: A Primer for Researchers and Practitioners. Australian Journal of Psychology, 71, 16-25. https://psyarxiv.com/a78g2/download