Well, yes, and you (or your computer) needs to be able to compute the reciprocal eigenvector of a large matrix in order to be able to use the Pagerank algorithm to search the internet. Should everyone be learning advanced scientific computing techniques and basic linear algebra before they use Google?

This is the car analogy again, and my point was that the car analogy fails. Unless, that is, you also think that the ability to parrot back the sentence "light is a wave" is the legitimate goal of education in physics.

School is not for learning lessons, it's for learning meta-lessons, if it has any purpose at all other than babysitting. If for some reason someone needs to acquire the actual procedural knowledge of looking something up in a specific kind of table, they can learn it on the job. What they need to learn in school are the meta-lessons that magic doesn't exist, curiosity is a virtue, and that they need to be wondering what parts things are made of. But if all you do is repeatedly teach them to follow sets of instructions without the appropriate intellectual context, then they will learn the exact opposite meta-lessons: that it's okay to have magical nodes in one's model of the world, and that they shouldn't ask questions.

You say elsewhere in this thread that you have no idea how programming works

Not exactly. What I actually meant by "I don't know anything about programming" was "I don't know any programming languages, and don't understand how instructions written in programming languages affect computer hardware."

It is both unnecessary and undesirable for everyone to understand everything about everything

My position is not "it is desirable for everyone to understand everything about everything". It is "if you don't know what an integral is, you cannot understand the subject of statistics".