Which material sounds better for speakers construction? Wood, Ply or MDF?

All speaker manufactures attempt to raise the resonance of their cabinets since low frequencies are extremely difficult to dissipate.

False. The thin wall, BBC-derived approach is to lower the resonance frequencies to the bass region. Since you like to reference Harbeth, read up on their philosophy.

Energy can not be destroyed. There is the challenge

True, but it can be altered, as into heat.

Lively Harbeth cabinets color the sound. Not the way I would build. 

Best materials are composite polymers. And this is not debatable. 

As far as I'm concerned, Wilson has this nailed. Goldmund used to use composite methacrylate in the Dialogues. 

Anyone building DIY cabinets can use Corian at the very least. It's not too expensive. Or anything from McMaster's catalogue. 

Well the Harbeth " model " is the exception. The resonance of MDF is low but their cabinets are thin and " loose " which raises the resonance, so they have chosen to lower it.
In most speakers  low resonance excite the cabinet creating a very large driver. We can all relate to the example of a car with the stereo turned up load. The bass gets amplified buy the body of the car, the doors which essential are the back of the cabinet become a huge " driver ". The area of the door, perhaps 20 times larger then the driver in the door when excited will sound 20 times louder the the driver itself. 

@soundsrealaudio

I see the confusion now. You're using the term "resonance" to refer to both frequency and amplitude. 

@helomech Thanks for the comment.  I am sorry the 1.7s did not meet your requirements.  I might suggest some agonizing reappraisal, to quote a '70s 7-UP commercial.

As you clearly understand, your ROOM is the most important element in any sound reproduction evaluation.  Possibly your room was not set-up correctly for the 1.7 experiment?  I will admit that this is a real chore and may not ever be right depending upon the room.  I have years of experience doing this and can state that there are some rooms that simply do not sound right with dipole speakers.  So be it!

HOWEVER, you seem to be an open-minded individual, so might I suggest that you give it another go at a dealer who knows what they are doing in their shop and listen again to a comparable model of non-box and box speakers in the shop where they are all set-up correctly?  You might be surprised at the quality of the sound, or not.  The objective, of course, is to make sure YOUR chosen system sounds the way YOU want it to in YOUR ROOM!

Cheers!