Be aware that measuring FR and THD is just that: measuring FR and THD: it's not a measurement of how good or bad something sounds. It's the equivalent of measuring a car's quality by looking at 0-100km times: it doesn't even tell us how fast a car will be.
There is of course room for individual preference, and one's hearing and the physical headphone fit play a role.
But essentially: yes, to a reasonable degree we absolutely can tell how good or bad a set of headphones will sound via measurements.
It's the equivalent of measuring a car's quality
by looking at 0-100km times
The "quality" of a car is the sum of hundreds if not thousands of factors.
Audio reproduction has basically a single input, and the output can be well described using a small number of metrics.
We know what sounds good to people. It would be a miracle if we didn't, given the fact that the business and science of audio reproduction have been around for 125+ years. It has been studied and is something of a solved problem.
Sean Olive and others have published some great research that's worth reading. The TL;DR is that headphone listeners prefer accurate sound reproduction that is fit to what is sometimes called the Harman Curve, which in turn correlates pretty well with the Fletcher-Munson equal loudness curve.
It's interesting that these debates pop up around audio but not video. We know what "looks good" in a television: objectively accurate color and motion reproduction. This can all be easily measured. Audio can easily be measured as well, and yet....
