I very much disagree with most of your examples. Most people don't seem to have a good sense for how associative memories work. The brain is so good at lying to us that we think we have all these discrete pieces of knowledge, but the reality from my studies is less reliable. When we 'learn' something, what's happening is that a bunch of neurons are being stimulated by inputs from all over your body. What ends up happening is you end up getting a neuronal pattern, that is largely repeatable given similar enough inputs (it's why we can roughly see images someone is looking at with fmri brain scans). But there is a problem when we 'learn' something, in that if we are in a different context and many of our sensory inputs are significantly different then we may be completely unable to recall the thing we learned, or be unable to apply that knowledge because not enough of the neurons fired to 'pattern match' our knowledge. What this means, is that if we want an instuitive understanding of something we probably need to have a lot of concrete examples to pull from, in as many different contexts as we can.

To get back to your gas pedal example. I'm fairly positive that the brain needs to map as many of the degrees of hardness of pressing to percieved acceleration as possible to get a good intuition as to the necessary force to achieve a given acceleration. And it's even 'worse' than you realize, because your brain also need to map out pedal depression vs environment (hills and turns effect acceleration), and depression vs car load. And, if you want to be a really good driver, collecting all this data in different cars.

Now we humans seem to have the ability to abstract away this underlying machinery to some degree, largely thanks to the wiring of our neo cortex, so after the age of 5 you can start to interpolate where unknown data points might lie on some spectrum given a few reference data points. But even then it won't be intuitive until we've done the exercise many times with different data.

I think when dealing with physical modeling of this sort, obviously we're going to need lots of examples to get a full enough picture of reality. I play ping-pong, so I have to be really cognizant of this, as my mind has to pattern match the way the ball works hundreds of times in a game.

But if I truly had to see the pattern on every single angle, every single type of spin, every different paddle, every different table, every different room, then the sheer combinatorial complexity would make ping pong impossible to improve at. Talking about and coming up with insights on better play would also be impossible.

It's relatively easy to break the symbolic continuities that the brain stores with new types of inputs. That doesn't mean those symbolic continuities don't actually exist and that the brain will constantly seek them out.