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.