Higher total harmonic distortion is an objectively less accurate reproduction of the original sound. But people can have a preference for less accuracy and that is not objectively “worse” except on one single scale that the consumer may not value.
Just like sepia toned prints are objectively worse reproductions of the original picture.
That's a terrible analogy, would you buy a screen that has a fixed perma-filter applied to every input? The whole point of buying headphones that are neutral and accurate in their frequency response is that you can enjoy different pieces the way you want. You can apply any "filter" you want to color an accurate and versatile speaker, but you can't get a pair of beats to clear up the mids or make the bass less boomy.
I said nothing about your preferences, that was the generic "you".
My point is good headphones are neutral and versatile enough that they can do both, just like a good screen can make all sorts of different pictures look good.
It's about versatility and quality in different dimensions, and headphones/speaker that impart too much color to music tend to be very one-dimensional which would limit what you can do with them.
Just like sepia toned prints are objectively worse reproductions of the original picture.