I’m no expert but I’m not sure that’s entirely true.
I did a listening comparison on a site that had recordings of different headphones. The recording would start with some kind of alleged reference sound. Then played from one headphone. Then back to the reference. Then another headphone. I thought it was really good. What I found was that many headphones did indeed color the sound. I didn’t want that effect. I found a brand that when listening, I could barely if at all discern the difference. That’s what I think might be thought of as flat. Which is what I wanted.
There are some audio pros around here. I’m not one of them.
The possibility of damaging your hearing I would leave to the experts around here. I’ll say it again…sure…people with not so good hearing can hear things when cranked up to high volumes. Is it good for them? Probably not.
I would say though that sounds above maybe around 7 or 8khz are really just harmonics of notes played at reasonably normal listening frequencies. Yes, to not hear them might make the original played note seem a little thin. But you would still be hearing the original note being played. This would be particularly so for natural acoustic instruments played without amplification. Electronic and amplified…all bets are off. Particularly if played back from a recording.