Ok, lets decompose that a little
I believe there is always a technical reason for an amplifier that sounds better or worse
Ok, so I think the word technical in the above is totally redundant, but going by what I think you mean, there will be behavior that any amplifier has that determines what the output will be like given an input and a load. That's entirely empirical and generally able to be measured. At the least we can subtract the input from the output and look at the difference, so we can see exactly what its doing at any time. But then you say "sounds", so that brings in two more unknowns, the transducer that converts the output of the amplifier to sound, and the ear and brain that listens to that sound and makes a better or worst judgement. Those two parts are far more uncontrolled and much harder to measure. But the amplifier, that easy. But exactly how do you suggest we measure "better", is your better the same as my better? Is your better today the same as your better yesterday? Once you find a way of fixing the right hand side of that sentence, I think making a amplifier that does it will be simple.
Rereading that, I will in fact say, there will always be a reason why an amp sounds better or worst, and some times the answer will be technical in that its something the amp is doing, but is also entirely possible to be one of many human issues that makes it sound better or worst.
you would think in this day and age, a simple subject like understanding a waveform whilst playing music would be common knowledge
I cant think why it would need to be common knowledge but in the context of analysis its generally well known. Again the problem is generally the part that isn't the amplifier. We can make amplifiers that have effectively zero effect on the sound, but in general people prefer them to have an effect, that's the problem.
As an aside a few weeks ago, I did a few searches on transistor grain
Well, first you would have to be sure that what you are describing as "grain" is a single thing, or if multiple, what parts are in it, but I think most of the answer you were looking for was in that John Curl video Mark posted.
a 32 page thread on diy audio produced nothing but wonderment at some of the posts
That's more of a comment of the social behavior of people on that forum than a commentary of the state of the art in amplifier design and understanding.
I don't want to sound all knowing (because I am not), but generally I think its perfectly possible to make a amplifier that is (to copy the word intentionally) to all intents and purposes blameless. There may be certain loads that makes that harder than others, and there may be other restrictions that also make that hard (must be efficient, must/must not use a particular device, must be a certain topology). And then we are back to the case where we want blame in the amp, because we like what it does. Or we may want to wrap marketing around it as a product, so we have to make it sound different to distinguish it from competitors. But generally I think all those are choices, not restrictions created by lack of understanding the problem.
In general I find the internet is not a great source of information if you just take random posts on a subject without applying some form of filtering. Just as true about audio as climate change.
Little known fact, coherent thought can destructively interfere with itself leaving no thought at all, that’s why I prefer incoherent thought.