Subjective vs objective is interesting.
The universe is governed by laws, not written but observed. As such it is all objective, everything that "exists" is objective.
"Life" is notional, virtual reality running on biological hardware, it processes the objective data and serves the signal inputs of all the sensors as a "subjective" input.
A lot of the basics have been covered, such as trying to reproduce signal input vs sounding good, so I won't cover that.
What I want to mention is subjectivity as it relates to the human mind and inevitably human and individual psychology. That is what determines what sounds good to an individual and there can be no universal consensus due to its nature. One might think this is good or bad, whether you'd prefer to have objective superiority to validate your equipment (and yourself) or be pleased that we are not assembly line products and that I am unique in either case you feed your self worth, the difference is how you do it.
Music,food,beauty its all the same, heavily influenced by our individual psyches and what has influenced us in our childhood.
In any case, the point of music is subjective in the end, objectively speaking one can analyze digital files to see spectral distribution of frequencies and in terms of objectivity it is just a bunch of random and/or patterned frequencies vs level vs time. It is irrelevant. Human voices sound different too because of various spectral distribution. For most people I imagine there are general distribution styles of frequency vs time vs level that appeal to them, you might know them as "genre". Certain other distributions do not appeal to them.
What makes this group of frequencies relevant? Our subjective perception.
But wait...to reproduce this subjective experience requires technology, understanding of universal laws and hence objectivity.
The problem lies that speakers are still often approached as an engineering problem. It is however not only an engineering problem but a psychological one as well on both levels, all of humanity as well as the individual.
The subjective and the objective must meet for there to be music in our homes that caters to individuals and for that individuals must involve themselves to understand what objective traits bring them subjective joy, be it a a sharp peak or dip or simply a ragged phase response or a lingering frequency somewhere that echos in time or a particular THD/IMD profile.
Of course most people do not want to involve themselves that much and simply don't grasp all these things. They have no interest in measuring and tweaking with DSP to achieve their personal flavor. Companies often take it upon themselves to impart flavor and the masses go along with it as they don't know any better. That brings me to the previous note that while speakers are not simply an engineering problem it is not practical for companies to individually tailor the sound for each speaker sold to each individual (discounting room and other equipment) so they choose a basic design philosophy in terms of subjective "sound" and use broad strokes to appeal to customers, make no mistake they are in it to make money, they couldn't care less whether you headbanged to Metallica or lost yourself to Beethoven or simply shook your head to the flat and flavorless appeal of your purchase as long as there is a purchase and you aren't returning it.
Most people in the world fit both subjective and objective categories, they want it to sound good to them with all the peaks,dips,distortions etc but yet they want to be able to claim to their peers that it is the "best" in terms of objectivity.
Since our world is now heavily rooted more in feeding one's self worth it becomes a question of do you show off the price tag, or the measurements/capabilities.
As to why we measure the audio? Most do it for self satisfaction that what we have is good. Because what we hear and enjoy is no longer enough, we need to be "right". Only those who know enough will measure it and only those who measure it will judge it, objectively. Ignorance was, is, and always will be bliss.
We are human, not machine.
Fortunate...or not, the tint of your shades will decide.