"Even though people cannot hear frequencies above 20kHz, it is important that audio equipment be able to reproduce higher frequencies to maintain clarity."
This myth is supposedly debunked with these words: "Fact: There is no evidence that a frequency response beyond what humans can hear is audible or useful. It is true that good amplifier designs generally have a frequency response well beyond the limits of hearing, and the lack of an extended response can be a give-away that the amplifier is deficient in some other areas."
This is really a good answer, though I feel not complete enough because it only hints at the truth. Let's look at what's being said.
When we use a single fact to prove a broad point we often lose clarity. Like trying to prove we don't have a large range of subtle tastes by pointing out the inadequacies of our taste buds and ignoring that taste is a combination of smells and tastes. We simply do not get the full picture when narrowly focused facts are employed to explain complex issues.
It is a fact humans do not hear much over 20kHz, even in the best case. So why should equipment with extended bandwidth sound differently than equipment limited to 20kHz? There are several reasons, one of of which is hinted at by our author, Ethan Winer. Any amplifier without extended frequency response is likely to have other issues that limit the response of the amp: aggressive input filtering, low slew rate, an output unable to follow the input, etc.
Another consideration that helps us understand why the opening statement is not myth, is phase shift. With few exceptions in filter design, a 20kHz limited signal will have major impacts on the preservation of phase accuracy at frequencies that are very much in the audible spectrum - and even small phase shifts are easy for the ear to detect when compared to proper phase in the same signal. IF a 20kHz bandwidth limited amplifier could be designed without phase anomalies, we might be able to accept that extending the frequency response higher would be unnecessary. But I have never seen any circuit without impact to audible areas of sound. It's one reason early brickwall filtering of CDs and output stages of class D amplifiers were so injurious to the music.
Rule of thumb: Extended bandwidth amplifiers generally have less impact on sound quality than their limited peers. As long as designers don't get too carried away extending the amplifier's bandwidth, more is better and certainly audible.