This study only looks at one aspect of sound quality btw. Namely, the frequency response. Which is certainly an important factor, but not the only I'd consider when buying a new headphone.
Other factors in sound that could influence preference have been researched, but I don't know of anybody trying to correlate that with headphone prices. There are several possible reasons for a product to be expensive. From the get go, only the brainwashed consumers that we all are, would assume a direct correlation between price and sound preference. Some headphones might be expensive because of the brand. Some might be done in small quantities. Some might use parts that are expensive to produce. Some might lead in specific aspects of fidelity but have a frequency response that doesn't necessarily please a majority of people.
About distortions and preferences, I know of 2 papers involving Steve Temme:
"A New Method for Measuring Distortion using a Multitone Stimulus and Non-Coherence"
by Steve Temme and Pascal Brunet
It's interesting because they suggest that there are more relevant measurements than THD. And also the method allows music as test signal. Which is an obvious advantage when trying to correlate measurements with subjective impressions of sound.
But I have no idea how to run such a measurement, and you won't see it used very often. Maybe it's not that relevant compared to FR, or perhaps it's not simple to do for the average Joe? I sure got overwhelmed by the math.
The second paper is:
"The Correlation Between Distortion Audibility and Listener Preference in Headphones"
Steve Temme, Sean E. Olive, Steve Tatarunis, Todd Welti, and Elisabeth McMullin
Here is a video on the second paper. A bunch of interesting stuff in that video IMO, if you can survive the very annoying sound quality.