How thick should the front baffle of speakers be?

Cabinet resonances can interfere with the output of the drivers in a bad way but they’re also unavoidable. All loudspeaker cabinets will resonate irregardless of the material but some less than others eg open baffles, transmission lines and some materials will have different resonances than others. Some designers prefer the sound of ply resonance to that of MDF but it’s largely down to application. It’s more of a question of exactly where you want to place those pesky resonances.

It’s very important issue because where these resonance issues appear when a speaker is operating at full or near full throttle can make or break a particular design. Some just totally fall apart.

It should be noted once and for all that a super rigid cabinet design is not the answer because as the OP points out, that usually leaves the internal box pressures with nowhere to go but back out through the cone as well as moving the resonances up into a more noticeable frequency range.

Midrange resonances, even mild ones are a sonic disaster because that’s where voices are and that’s where our ears are the most sensitive!

So thicker cabinets are not without compromise.

So as often is the case with loudspeaker design it’s a question of choosing where to place / balance / hide those inevitable design compromises. Some designs are cleverer than others at doing this, no doubt.

Harbeth employ a lossy cabinet design which supposedly dumps these resonances below the hearing threshold, but that’s just one approach amongst many. They seek the cleanest midrange performance possible but it also has its compromises as they freely acknowledge their speakers may not be the best for Heavy Rock or Metal etc.

Horses for courses as usual.

Uh, that’s one of the main benefits of isolating speakers - to remove the cabinet resonances. The other main benefit is to eliminate mechanical feedback via the floor. Problem solved! 🤗

There used to be a loudspeaker manufacturer named Hales that featured ultra-thick front baffles-I believe of birch ply. They were reviewed multiple times by Stereophile. As with any loudspeaker, they still had strong points and weak, and the company ultimately folded.
There have been tiny loudspeaker ventures in the past that featured cabinets made of concrete. They failed for obvious reasons.
I listened to Magicos extensively at this year’s Axpona in two different rooms. They sounded dull to me. Not terribly dull, but not worth the long green.
I am of the humble opinion that there is simply no one single design approach that solves all of the problems inherent in loudspeaker transducers. I also happen to think that there is a large segment of the audiophile community who wish to believe that cutting edge technology is the path to loudspeaker-happiness. Exhibit A is Kalman Robinson of S’Phile. Take a look at this months edition of his column. KR is indisputably 100% correct as to his choice for himself, but one has to wonder how much of his opinion is based on the real versus the perceived versus placebo. Put differently, would he like his choice of loudspeakers just as much if he were blind? How about if he had no preconceived notions?
There can be no argument that loudspeakers-every design currently known to mankind-introduce more distortion in music reproduction in the home than any other component in the chain assuming lack of glaring defects. Eliminating cabinet resonance does not change that fact. Loudspeaker distortion has to be managed because it can not be eliminated.

Back in the mono days (well before Thiele-Small ) I built a woofer using two 15" JBL drivers mounted on a sand-filled plywood "sandwich."
Getting the back panel of the "sandwich" not to leak the sand turned out to be a problem.

Sound? Yikes!

fsonicsmith, it does not have to be eliminated. There are two types of distortion, Linear and non linear (this is psycho acoustic babble now, not my own) Linear distortion is alterations in frequency response which are very noticeable. Enclosure resonance would be in this category. Non linear distortion is IM and Harmonic distortion as well as mechanical distortion, buzzing, rattling and so forth. Studies (not mine) Have shown that Humans will tolerate non linear distortion levels up to 20% under certain circumstances the reason being that the distortion is being masked by the music. Non linear distortion is also more noticeable at lower volumes. This could be why some of us like higher volumes until system overload. This is the reason MP3 files sort of work. 
Frequency response is now completely manageable in the digital domain. You can correct virtually everything including enclosure resonance with room/speaker control. And, according to the psycho acoustic folks non linear distortion does not matter that much until it reaches ridiculous levels. Probably why we tolerate listening to such crude devises as loudspeakers. I guess their message is get full spectrum room control and be happy.......right.