Note that sound signature isn't just a brand thing - it's a product of price point and profit margin. The lower the price point, the more compromises to the design, and so they compromise on a sound that is acceptable for that profit margin to define the brand and go all out with what they really want at a much higher price point. Look at how different the HD650 and HD598 are vs the HD800, or how much the DT990 differs from the HD600 a lot more than the T1 from the HD800. Still, it's not perfect - there are still some influences from the marketing and sales departments considering these are big business right now with a rising headphone market, unlike when Chrysler said, "luxury sedans only!" then Jag engineers walked out a barn, working on their own weekend time, with an XJ220 (remember that Chrysler also owned Lamborghini at around the same time before they sold both).
In any case, as per the prospect of "hi-fi" being a real thing - has any headphone, including your friend's, measured as flat as an amp or DAC/CDP? Because that has been the problem for the longest time - designing a speaker or headphone system (not just the driver, but the cabinet and cup.chamber, the earpad, etc) that measures as flat as what we can get out of the electronics. Even then, if one measures whole systems, changing an amp can change the sound, not because the amp is EQ-ing it but measuring flat doesn't necessarily mean it can drive a headphone playing music, which is nothing like a sinewave used for testing. You use a sine wave and at any moment there's one frequency playing, and slightly more (at a given second) if it's a sweep. Music at any moment can have too much stuff going on and we expect all of that to sound "natural."
The bigger problem is people's perception of "natural sound." I've had people tell me my headphone system isn't warm enough; however the conductor of the local orchestra thinks there's nothing wrong and their idea of "warm enough" sounds nasal to me even on the jazz they're listening to.
I agreed with you. Speaker and headphones are not accurate yet. There are way too many variables. Even your bone structure will affect the sound. Maybe one day there is a technology that can provide a feedback loop that altered the sound characteristic. But is there an incentive to make them more flat, or is there an incentive to make them more bass heavy like the Beats. Beats are outselling all other phones combined with a hefty price tag. If I am the headphone manufacturer, Beats will be my target. They will be the new "hi Fi" standard.
A closer example will be amplifiers and cable. Modern day amplifiers are as flat as a ruler. Cables for sure is flat. But if you read the reviews, even USB cables have house sound. It is obvious that you can make an amplifier to have a house sound. But is this Hi-Fi? So, if I read enough review, I would have come to the conclusion that audiophiles do not like Hi-Fi or anything that sounds alike. It seems that they would pay extraordinary amount just to get something different or something marketed as different. Somehow that "assumed" difference is accepted as high performance/Hi-Fi. Blind test are never used in any review. What if they actually sounded the same?