A few days ago, I read an interesting interview with Goran Tomljenovic, Croatian designer of ultra-high-end loudspeakers and I found in the article some interesting facts that are in some way related to your debate about how different materials affect the sound quality of the saxophone. Goran’s speakers are interesting because they are in principle a horn loudspeaker which as main element uses an acoustic horn, as well as many brass and woodwind musical instruments (link: https://www.facebook.com/Ring-Audio-159138464215165/ ) Those speakers (Ring Audio’s Master Horn Jazz - MH Jazz to acquaintances) are very nice, but also very expensive and cost around 20 thousand US dollars.
Asked if the material was important for sound quality, Goran was very clear. He said that their horn loudspeakers are made of different materials - wood, composite materials, ceramics, ... but it does not matter to the sound quality at all.
Moreover, he emphasized that it is only important that the material from which the horn is made must be, so to speak, “ACOUSTICALLY DEAD”, i.e. for the material itself it is crucial that its resonant frequency is BELOW THE AUDIBLE LEVEL. Also, the material from which the horn is made, must not affect the resonance of the air INSIDE the horn channel.
The only thing that matters to acoustic horn is channel shape, high measuring accuracy, and great precision craftsmanship. This is quite opposite to the many other musical instrument. Usually, the instrument box (body of the instrument) must resonate so that we can hear something at all.
For example, the guitar string causes the soundboard (upper and lower plate) and sound box to vibrate, and they strengthen the vibrations of the strings and amplify sound. With the acoustic guitar, the choice of materials is crucial for the sound quality. For saxophone, the material is not important for the sound quality, this is more important for durability, playability, wear resistance, corrosion resistance, etc. And of course, for seller marketing tricks. Here I must quote Stephen Howard who wisely commented on another forum where there is a similar discussion of whether the material affects the sound quality of sax:
“After decades of comparing otherwise identical horns - the only difference being the body material - I’ve come to the conclusion that the answer to this thorny question is - Yes...but only if you’ve paid more for it". Same as with wine. If the price on the wine bottle is higher, people like it more. Even when all the bottles that they have tested, contain exactly the same wine.