Regarding "growth triplets", I propose that you only stop at 3 because it's a nice number. Consider mathematical approximation, where your first guess might be too high, then your second correction too low, then third too high again but much closer to the exact value, than the first one, and so on to infinity. The general idea is that increasingly better models can sometimes oscillate with respect to certain metrics. I think the idea is trivial, and I think your stopping at 3 may indicate some confusion.
Humans are not thermostats, and they can do better than a simple mathematical model. The idea of oscillation with decreasing amplitude you mention is well known from control theory, and it's looking at the phenomenon from a different (and, I dare say, less interesting) perspective.
To put it in another way, there is no additional deep understanding of reality that you could use to tell apart the fourth and the sixth oscillation of a converging mathematical model. If you know the model, you are already there.
I'm becoming less sure of this, but let me explain.
Now I actually tend to use the number 5 and sometimes even 7 rather than 3 because there is stuff going below the level of adult human that is sometimes worth talking about, but if we take our starting point as adult humans and their naive perspectives then I think 3 is fine.
So what I've thought for a long time is that at 3 we get enough to form stable loops that short circuit the need for more levels. You give one of my favorite examples of this in your piece—thesis, antithesis, synthesis—which forms a loop and doesn't require more oscillations because you can just make the synthesis the new thesis and repeat to refine without needing to see deeper. Some folks around here know this as the "you don't need more than 3 levels of recursion" heuristic.
However there are times when you may want to manipulate the loop itself while also working on it at the object level. I sometimes find myself wandering in this direction during meditation but find it hard to do because it's asking me to keep a lot of stuff in working memory at once. It may turn out that I can't actually do it or take advantage of another oscillation/level/etc., but I do find myself wandering that way. This is not to dispute that 3 is not enough, only that having more may enable experiences that would otherwise be too complex to have without the aid of memory.
What do humans do better? In what ways are human oscillations more interesting? What is the deep understanding of reality that lets you tell apart first and third oscillation? Honestly, I have no idea what you're talking about. Maybe "less interesting" hints at mysterious answers?