I heard these same arguments when I started calibrating my speaker system. A lot of it just isn't true.
First of all, frrequencies are sound, and flat response is natural sound. An acoustic violin playing on a recording has the same response as an acoustic violin playing live in the room. Balance the volume levels and dynamics, eliminate distortion and push the noise floor below the noise floor of the room and they sound *exactly* the same. Audibly flat response is audibly flat response. If an acoustic violin in person sounds exactly like an acoustic violin recorded, the response is by definition flat. You don't have to apply any corrections. Flat response is critical in acoustic music like chamber music, acoustic jazz and orchestral music. Those of us who listen to live music know instinctively what those instruments are supposed to sound like. (It doesn't matter so much in music where all the musicians plug in, because there is no baseline of "realistic sound" in purely electronic music. But it's still best to be accurate to what the sound engineers intended the mix to sound like.)
Secondly, many of the problems with sound reproduction trace back directly to response imbalances. Frequency masking can mess up clarity and transparency. Masking can also hide the aural cues that indicate depth in a recording. Noise levels in historical recordings are exaggerated by headphones with boosts in the upper mids to give "in your face" sound. Frequency extension is a lot less important than frequency balance to sound quality. If you want deep bass, start with balanced bass.
Thirdly, our sensitivity to frequency imbalances increases as the volume increases. Big spikes in the response in the wrong range can massacre your ears. That's why you EQ in passes, from lower volume to high. If you have time and want to do a really precise job, you start at a low volume and work your way up an octave or two at a time in mmultiple passes until you get to the maximum volume level your ears can stand. But that is going to be a louder sound level than unbalanced, because you don't have a nasty spike sticking up 20dB to shred your ears any more.
Lastly, no matter what your hearing is, flat is flat. If I can't hear about 17kHz, don't ask me to EQ the stuff at the edge of audibility for you. But in the core frequencies, humans are pretty doggone consistent. Even if we weren't, it wouldn't matter because flat response with whatever our ears does to it is exactly the same as natural sound with whatever our ears do to it. Natural sound is natural sound, no matter how we perceive it.
Achieving a balanced frequency response isn't easy. Throwing money at the problem won't fix it. Expensive transducers have the same problems midrange ones do. It takes research and hard work. Figuring out how a parametric equalizer works can be very non-intuitive and difficult. But a balanced response is natural and present sound. It is achievable. And balanced for me is exactly the same as balanced for you.