The analog part between the DAC and the amplifier is important on the sound and is deceived in the AV receiver. If you rely only on measurement, see. this
https://www.audioholics.com/audio-amplifier/audio-amplifiers-sound
SR8015 is the first for which a squarewave was measured and only from the preamplifier. The result is terrible and is considered a good feature. When a preamplifier does this, what does an amplifier do? And now imagine it with a cheaper receiver.
https://www.audioholics.com/av-receiver-reviews/marantz-sr8015/conclusion
Those are excellent reads, and thank you for posting the links. On the square wave thing, in my opinion, technological advances have rendered it practically irrelevant, especially on the preamp side that you are talking about, at least not really an issue for mid range gear such as the ones this thread is about. Stereophile has been doing the square wave measurements for a long time, and I don't recall JA worry much about any of those measured in practical terms. Surely some measured better than others, but the fact that we can't hear much above 20,000 Hz, let alone 30,000 Hz and higher, the difference would not likely be audible in most cases, or at least nothing so audible that can explain claims of night and day difference (not you, but I remember reading such claims on forums, probable even right here on ASR) anyway.
In one of the embedded links in the ones you posted, there is a paragraph in one of the article that I would like to quote:
The Sound of Audio Amplifiers: Can you hear a difference between Amps? | Audioholics
The possible reasons that amplifiers had specific sound characteristics were becoming a popular topic among audiophiles in the early 1970’s. There was a 1973 meeting of the Boston Audio Society that featured a presentation by a test equipment maker (I forget which) that could display the spectral characteristics of an amplifier’s THD. This was pretty heady stuff in the early 1970s. A very popular receiver at the time, the Marantz 2270, was well-known for sounding harsh if pushed too hard. At this BAS meeting, we found out why:
Even though its actual distortion rating was low (probably 0.3% THD @ rated output), the scope/analyzer showed that when it hit its clipping point, the Marantz exhibited large amounts of higher-order distortion products.
As we know, harmonic distortion is the unintended signal products generated by an audio device such as a speaker or amplifier that are whole number multiples of the original signal. For example, if an audio device is tasked with trying to reproduce a 40 Hz signal, and instead produces 40 Hz and a small amount of 80 Hz, the 80 Hz product is called harmonic distortion. Small amounts close in multiples (lower-order) to the original signal are barely audible; larger amounts of distortion in greater multiples away from the original signal (higher-order) are grossly objectionable to the human ear. (Remember the harmonic structure of Western music is based on octaves and 3rds, so 2nd and 3rd-order distortion is harmonically-related to the music in a way that we do not find dissonant or audibly offensive. Lower-order THD has to be pretty significant before we notice it in a negative way.) The sum total of all harmonic distortion products is usually expressed as a percentage of the original signal, or % Total Harmonic Distortion (% THD).
On the scope, we could clearly see that the Marantz produced large amounts of 4th-, 5th- and 6th-order harmonics when it was pushed into clipping. A Pioneer receiver there for comparison was better behaved and its distortion was composed mostly of 4th-order and lower components. An AR receiver showed by far the best distortion behavior, with most of its harmonics being very benign-sounding 2nd- and 3rd-order products. Now, finally, there was a concrete, repeatable, tangible explanation for why some amplifiers sounded better than others when pushed into clipping.
The hearsay about Marantz being "warm" and "musical" sounding was likely due to receivers and amps in the late 60's to 70's when it is rare to find SINAD higher than 90 dB, my SC-7 and SM-7 were close but still below 90 dB. The popular 22X0 receivers, as the article alluded to, had their THD specified in the range of 0.3 to 0.5% (the 2230 for example). So yes, they could sound different enough to be labelled with all sorts of sound signature, I guess.
Today's gear, such as the Marantz models measured by ASR, all have much lower THD+N, so as long as you keep them well below their output limit, you shouldn't have to worry about their bad (and different) behaviors pass their clipping points that the above article referred to.
Square waves, like damping factor, amount of negative feedback, TIM distortions are really not that relevant any more in most cases. If they were, I am sure Amir would include them in his measurements (I would welcome that even if he would only consider it, but it's probably too work for him..).