When it gets to the point where you can measure timbre directly, my guess is that it will transform speaker “measurements” and timbre will be incorporated in measurements in a meaningful way.
This is all measurable and can also be made visible in various forms of visualization.
The problem is really not measurability.
All of the Field of Audio can be measured today, but you also have to be able to interpret it.
In the field of loudspeakers, the basic technology has basically not changed since the invention of electrodynamic loudspeakers by Edward Kellogg and Chester W. Rice in 1925.
A modern BMS or Purifi driver is based on the same principles of the spring mass system.
Evolutionarily improved, but the same principle - with all its flaws and measurable limitations.
There is some research in other directions, like MBL and Manger or the Plasma Ion Tweeter, but basically the speaker in most living rooms is the same old principle.
It would therefore always be necessary to measure the living room with the specific loudspeaker in order to arrive at truly enlightening measurements.
This is being practiced more and more with amplification and DSP support.
Incidentally, this has been common practice in PA technology for a long time.
In any case, I always have to smile when someone talks about a value of at least 120 Sinad and the situation then shows the great DAC in combination with two small loudspeakers in a resonating shelf.
Because every angle of change in speaker position, every change in distance, every turn of the head, every item lying in the acoustic path, every cushion on the sofa, every wall hanging, every glass door in the wardrobe, every carpet, every room resonance and above all every single wall made of stone or a resonating wooden frame with damping filling makes a far more significant and, above all, audible and measurable difference than the difference between 90 and 120 db SINAD at an Digital Audio Converter.
Pushing the limits of what can be measured in audio technology out of the audible range makes sense, but only if the same effort is put into the fundamentals of room acoustics.
The room interacts with the loudspeaker and I would go so far as to say that the listening room is part of the loudspeaker itself.