How thick should the front baffle of speakers be?

Well I dont think a speaker can sound accurate with one genre of music and not another. Harbeth's lossy cabinet represents the worst possible approach to this problem in my opinion. 

jsautter,
I disagree.  The Harbeth SuperHL5plus that I owned sounded excellent with all genres.  A very balanced, neutral and revealing speaker (which employed it's lossy approach to actually achieve this balance).

I have to agree with jsautter with respect to lossy cabinets. It’s an attempt to make the cabinets sounds “add” to the drivers output in a perceived pleasurable manner. My (admittedly) personal preference is a design that minimizes the cabinet’s -specifically the baffle influence on the overall output.

To the OP, how do mere moving pieces of moving paper cause the your pant legs to flap? The answer is it’s a sum total of the amp, speaker membrane, voice coil, magnet, cabinet and room interaction. 

Harbeth owners no doubt like the way their speakers sound, but on the larger models the resonant cabinets impart a sound that isnt on the original recording. All speakers do this, but on the Harbeth models I have heard this flavor is very apparent. So I naturally object to those that think these speakers sound natural as I hear the extra "gravy" as a distinct coloration. Just my take.

Mmmmmmm… g-r-a-v-y. It sounds delicious...

I understood that Harbeth's design goal was to make speakers that do not store the energy radiating from the rear waves of the drivers ( not the same as vibrations from the movement of those drivers). To this end the design is a success. The design would not seem to be as successful with the large woofered 40's.  I would doubt they intended to make their cabinets sing. 

Thinking Nicki Minaj, Taylor Swift ??

A singing cabinet is the natural and unavoidable byproduct of a thin walled cabinet. If this singing is pleasant or not is another issue altogether. Mr Shaw can can say whatever he wants about design goals and perceived sonic realities but the fact remains that this method of dealing with energy makes no sense to me and if you listen to a Harbeth speaker you may hear exactly what I am discussing. 

I have listened to the Harbeths. They are not perfect and I think there are probably some frequencies that do tend to excite the cabinet. On the other side these heavy MDF cabinets store low bass energy and then release it slowly with a noticeable dead sound, the kind I do not care for.