That's a very valid point, but what I remember of modern language teaching at school (French in my case) was very utilitarian. Just lots of vocabulary, conjugation rules etc. to memorise - all how to speak the language but very little as to why you'd want to bother and little of intellectual interest. Latin was better, in that we actually looked at examples of Latin literature and poetry and the Roman civilisation. Shame the language was much harder, with all the noun declensions and so forth.
All a bit of a waste really, as there's a lot of interesting things to learn about languages. The scientific side - how they evolve over time, how various languages relate to each other - cognate words, sounds shifts etc. And the literary/cultural side for those that way inclined.
In any case, I can't see anything that programming languages have in common with natural languages besides the word "language".