I am in favor of letting [h] and [ɦ] stay where they are as glottal fricatives—honorary glottal fricatives, if you like! What the preceding paper says about them is true—there tends to be noticeable glottal turbulence with [h] only occasionally, particularly before open [a]-type vowels (or after them, in languages with final [h]'s). The voiced counterpart is perhaps more likely to have some turbulent glottal flow, being, in fact breathy or whispery voice. My reason for wanting to keep [h] and [ɦ] in the chart is perhaps more phonological and practical than strictly phonetic. There are so many languages in which one or both of these sounds functions as a syllabic margin—as a term in a series of consonants—that one often wants to put them in a chart of consonants. In Caucasian languages [h] often coexists in the consonant system alongside [ʔ], and (e.g. in dialects of Agul) alongside [ʔ], [ʡ], [ħ], [ʕ], [H] and [ʢ].