Since you said that you have heard "amps with higher distortion that sound more musical"...it would be up to YOU to explain what you meant by "higher THD", not me.
It's been evident for quite a few years now based on psycho acoustic evaluations that it's not just the quantity of distortion, but the type of distortion that matters. In essence, high levels of even order (e.g. 2nd, 4th) distortion, even when audible, are quite tolerable and actually enjoyable. High order odd harmonics, such as 9th, are detectable at even very low levels, and degrade the sound. There are reasons for this, but to encapsulate it's all about the non-linear response of the auditory system and "masking" that occurs. 9th order harmonics can be detectable, by trained listeners, at levels of 0.05% or even lower, according to some studies.
This is, alas, exactly at the point where amplifiers that employ negative feedback often are problematic- especially those that are bipolar based. This is due to three mechanisms- the non-linearity of the amplifier output stage (so called crossover distortion), the non-linearity of the input stage that processes the feedback, and the low levels of corrective feedback that both increases the signal applied to the input (both musical input and feedback signals)- creating more distortion- and reduces the amount of correction that can be applied.
In addition, high frequency non-linearities that are not captured by the usual 1kHz THD spec can cause intermodulation of complex signals like music and degrade the effective S/N ratio, leading to a loss of resolution and clarity.
These are probably the two principal reasons why relatively high distortion open loop designs sound more transparent and pleasant than the more common moderate global feedback designs that are customarily employed.
Very high levels of broadband negative feedback or complex feedback/feedforward designs can overcome these limitations and produce ultra low distortion, very neutral sounding, amplifiers.
So, amps that have "low" THD measured at 1kHz can sound terrible, while those that measure much worse can sound far better.