I don't see it as nitpicking, but as clearly stating my opinion, which I think does differ from yours in some significant ways. Which is totally fine by me. We don't have to agree on everything. (I rarely do with anyone anyway.) Does it matter? Well, we're discussing this on a board which primarily functions as a way to find people to exchange money for sex, so I'm gonna say probably not so much.Does it matter if we are not completely the same page with this or any topic? Not quite sure why you need to nitpick on people that basically agree with your overall argument that there are multiple ways to look at problems. I would agree with you though that memorization and repetition go hand in hand. On the other hand, that process can be very frustrating and time consuming and that's where teachers, tutors, etc need to step in. IMO, I think understanding what exactly is happening when you do any numerical operation vs memorizing that 3 x 3 = 9.
Perhaps we need to step outside of math for a moment. In computer programming, there's no way you could memorize enough code. The field is too broad and ever changing. Instead, you learn some core concepts like variables, loops, functions, etc. that are basically the same no matter if you're writing Python, JavaScript, jQuery, etc. For everything else, you have books or Google to rely on. There are lots of differences between them, but the core logic is basically the same.
You're clearly knowledgeable in mathematical concepts so how about describing their practical application? How do the quadratic equation, factoring trinomials, etc. apply practically? I feel that most of teachers don't even know because they were also taught to memorize these concepts. Perhaps we need to be teaching math and some basic computer programming concepts at the same time so that students can visually see what is going on?
Specific applications is always a bit of a black hole, since I think there's a lot of value in studying math whether you're concerned with specific applications or not.
However, when it comes to quadratics, there are certain things in nature and finance that behave in a quadratic fashion, like the height of a projectile (barring complications like air resistance) or profit functions in certain specific scenarios.
Factoring is largely a tool that you build on for other tasks. It is crucial for many cases in solving equations, deriving formulas, proving identities, simplifying expressions, analyzing functions and the like.
If you move up a grade level or two to stuff you first see in grades 11 and 12, you will probably find more interesting applications. Tons of stuff in the world can be modelled with sinusoidal functions: sound waves, predator/prey population patterns, circular motion, and the like. Series have all sorts of direct applications in finance such as annuities. There are some classic examples of exponential functions such as radioactive decay. For anyone interested in game theory, many game mechanics can be modelled in these kinds of ways.
One thing to keep in mind is that many phenomena in the real world are combinations of various components that might individually behave in different ways. These are known as complex systems, the study of which certainly relies upon the basic building blocks of the kind of material one studies in high school math, but requires more sophisticated knowledge. Some important examples include economies, the environment, and (what might be of particular note right now) the spread of disease.