[nandemo]

What makes a frequency response "good" is subjective. A lot of audiophiles prefer flat, but many like e.g. tube amps, which aren't exactly flat, or headphones with V-shaped frequency response etc.

> meaning that a "flat" or otherwise non-average frequency response would distort music in an unintended way.

Not sure how to make sense of this. A flat frequency response is by definition the one that does not distort the recorded music.

If for the sake of the argument bass-heavy headphones and speakers were all the rage and a sound engineer set out to record music compensating for such devices' frequency response, then they wouldn't sound "bass heavy" anymore.