the number of potential variables involved in making a scientific study of the effects of mouthpiece material would include
- making several identical mouthpieces in a variety of different materials. Exactly how you'd make accurate measurements of the internal shape of a mouthpiece is beyond my comprehension
- positioning the ligature and reed in exactly the same place on each mouthpiece and tightening up the ligature to the same tension
- placing your lips on each mouthpiece in the same place
- shaping your embouchure in the same way
- standing in the same position in front of the measurement microphone
from what I've observed, no acoustic instrument will ever make exactly the same waveform twice - the phase angle between the harmonics is always slightly different and constantly changing
as players we perceive the sound differently than a listener or microphone - we hear by bone conduction as well as the sound in the air and the different densities of brass, silver, hard rubber etc will affect the way the sound is conducted to the eardrum.
I've found that the same mouthpiece and reed can sound different from one day to the next and I use synthetic reeds and leave them on my mouthpiece, so no variation of ligature or reed involved.
I have recordings of myself playing different makes of mouthpieces and saxes with quite different sounds when I'm playing them and I can't tell them apart on the recordings.
While it's quite possible that mechanical properties of the material a mouthpiece is made from may have some effect on the sound, I'm inclined to think that the effects of my embouchure overwhelm any subtle effects of the hardness and density of what the mouthpiece is made of, or what the sax is plated or lacquered with etc
Other people may have different experiences - we're not all the same.
If someone finds a metal mouthpiece to be different to an ebonite one, that's fine, but not everyone will have the same experience.
This is why I try to stay out of discussions on subjects like mouthpiece material, ligatures, reeds, effects of silver plating, lacquer etc. Without hard data it's just one person's word against another and it soon becomes divisive and yields more heat than light.
If having a new mouthpiece enhances your playing experience, that's good. Being quite happy with what you've got already is also good. In general I've found that happiness is a good thing - happy new year!!!