Is it just me?

So this doesn't necessarily pertain to Chinese; it can be applied to any language.
Is there a reason that language classes aren't taught as we humans naturally learn? Why is it reading and writing and speaking and listening seem to all be taught right from the beginning in unison? Like, we learn to listen and understand first and then respond through speaking while we're infants. Therefore, why do teachers not focus on that mimicry first and then after a couple weeks or something move on to teach the alphabet (or for Chinese the radicals which are the basic building blocks of characters) and then the common and/or simple words? Wouldn't be more appropriate to follow the steps in which we naturally learned our own language?
Going back to my experience learning three different languages (which I first mentioned in a previous post), let me further explain them since I've been taught by more than one teacher for all three. I had 3 different French teachers, 2 different Japanese teachers, and 2 different Mandarin teachers. They've all been taught with everything beginning in unison. This just seems to be how it's done in all language classes. The only exception I can think of would be my first Mandarin teacher, Fu Laoshi, [laoshi, or 老师, means "teacher" and is always behind the surname] who spent two weeks explaining the different tones and forcing to be able to hear the differences between them and be able to produce them. Why is this not the norm?
I'm just wondering if there's research to say this doesn't work or if it's just because of lack of time. You would think after being taught in 4 different schools, two of which were colleges, I would have witnessed some major differences in styles of teaching. Anyone have anything? Otherwise, I'm about to make it my mission to become a teacher and teach a language this way and see what happens.