How thick should the front baffle of speakers be?

Some manufactures advertise or hype a thick front baffle, two layers of MDF,  if the woofer is as thin as  paper cone how could it change anything. Could be just hype
I use 25mm Baltic Birch for every motorboard I build and if the area of the sides is large there too. Really tough, no outgassing or fear from water damage like MDF and no voids if you stay away from the Chinese stuff and use only real Baltic Birch. Reverberation happens more than people think and thicker plywood is a great answer. Build your cabinet right and all the bandaids for poor cabinets like expensive feet are not needed.
Materials make a difference. Thickness makes a difference.

Just because JBL and Altec used to use 3/4 inch ply, does not mean it was the best material. Testing methods, building methods, material availability, construction methods, etc, were nowhere near as advanced as they are today.

Speaker and cabinet technology has come a long way. Driver materials have improved (less resonance, better damping, less flex, lighter, more rigid, etc), speaker cabinets materials have improved (constrained layer damping, less resonant, better damped, composites, CNC construction for better shapes, etc, etc).

I can speak from direct experience. I have a friend that used to be a speaker designer and builder. I used to help him out. Several of his designs were bought be some pretty well known companies.

When he was designing a speaker, he would build it in a real basic box, just to get it close to sounding correct. Once he got to the point where is was very close, he would then build a box using CLD, with thicker materials and baffles, and the improvement (without any other changes) was not trivial.
The aluminum front baffles are interesting like kef ref and elac adante without having to go full aluminum. Ascend acoustics uses bamboo which is also very stiff.
and the improvement (without any other changes) was not trivial.
wheres the proof
wheres the proof

In extensive notebooks and old hard drives.

I just contacted my friend (he's now a major audio/video integrator in L.A.). He reminded me, that not only were the improvements audible, but they were measurable. 

You do understand that there are many tests that can be run on speakers, drivers, cabinets, crossovers, etc, that have direct correlations with sound quality, right?

Pulse tests and waterfall plots were noticeably better in deader, less resonant cabinets.

I don't even understand why this has to be explained? Build a cabinet with less resonance, that is better damped, and the entire speaker system has less resonance, and is better damped. 

The fact that YOU do not understand the types of things that make speakers sound better, is not my concern. The fact that you don't even own a system, and are commenting the findings (subjective and objective) is quite laughable.