Everything we hear extends from the pressure the drivers exert on the air. I do think we can measure everything. I also think we underestimate how audible some differences in measurements are (and we overestimate others).
I already admitted that all differences in the sound of a loudspeaker could be measured in theory. But in the real world that is not practical and for all practical purposes not even possible.
Immanuel Kant (1790-1835) inaugurated a Copernican revolution in philosophy, when he claimed that the subject doing the knowing constitutes, to a considerable extent, the object—i.e., that knowledge is in part constituted by a priori or transcendental factors (contributed by the mind itself), which the mind imposes upon the data of experience. Far from being a description of an external reality, knowledge is, to Kant, the product of the knowing subject. When the data are those of sense experience, the transcendental (mental) apparatus constitutes human experience or science, or makes it to be such.
What does that mean? It means that not everyone hears the same, and certainly not every human (much less other animals or humans as they evolve) hears the same as instruments "hear" things. The differences in hearing ability is much wider from person to person than most people realize, and even if two people have the same measured hearing ability (almost always measured with headphones), not everyone has the same size, same shape, and same angle of their earlobes. Try cupping your ears with your hands when listening to music, and you will probably find the difference to be astounding. This subjectivity, especially with regard to speakers, obviously goes way beyond this, such as how the listening room (not just our ears) vary from one to another, or from one place in the room to another, etc, etc. The permutations are infinite,
Then there are complexities of measuring the speaker system itself. Almost all measurements that I know of are done a single frequency at a time. Even a frequency response curve is done with a frequency sweep, but measuring a single frequency at a time. But in music, there are almost always going to be multiple frequencies coming out of the same driver at the same time. This can drastically alter the performance of a speaker driver, and the speaker system.
For example, when Amir (ASR) evaluated the GR Research LGK 2.0 (see link below), he noticed
during a listening test (some on this forum claim Amir doesn't think listening tests are useful, so I guess he was forced to do it at gunpoint), that when a female voice and a bass note were playing at the same time, this single driver speaker system completely fell apart, even though it measured well and sounded good when the individual notes were played. So how would one measure this? Yes, some objective tests could be devised to measure the distortion when multiple frequencies are playing on the same driver, but there are an infinite number of different frequencies (and an infinite number of combinations of frequencies) that could be measured. And even if that could be done, how would one know which where the most important combinations, and which were unlikely to make a difference with real-world music (not to mention that not all music has the same frequencies, and people have different music preferences, and there are big differences in the hearing ability of people). So all this talk about objective testing is fine and very useful, so long as one does not take it to the extreme and erroneously believe that measurements represent some kind of absolutely true and objective testing that can always be relied on to determine the differences in speakers.