I don't necessarily have an objection to some form of coding requirement. However...
So, if you look at the foreign language requirement for what it is (an "expand your mind" requirement)
"Expand your mind"? That's really vague. Just a few things foreign language requirements help with that coding doesn't:
-- English grammar and usage. Many good writers and speakers have noted that they first really understand grammar and details of English usage when they study a foreign language. Now, of course it's possible to refine one's language use without formal grammar training, but the process of deconstructing a foreign language is often helpful to understand one's own.
-- English etymology and vocabulary use. Particularly if one studies Latin-based language like Spanish, French, or Italian, one gains knowledge of Latinate roots, which are often helpful in figuring out Latin-based English words. Frequently in the first few years of language instruction, you'll learn a lot more English vocabulary through relationships with the other language. Germanic languages also are helpful in learning new English words, due to common older roots.
-- Communication skills. A lot of students who just take a couple years of a language in high school or whatever don't really get a proficient speaking level, but that's largely due to lack of practice and subsequent failure to "keep up" the training. Nevertheless, for many students who do take the oral skills seriously, languages like Spanish can be incredibly helpful for communicating with customers/users and other job contacts in many professions. If you have an opportunity, doing something like Mandarin or Japanese can open yet other doors.
-- As one learns another language, generally one learns about other cultures too. Which again is often an introspective exercise in learning about your own culture -- you don't realize your assumptions about the word often until you contrast them with someone else's. This can be a very eye-opening exercise for young people.
None of this is an argument against coding. But there are more specific things language requirements do, aside from basic skills in that language or "expanding your mind" (whatever that means).
I think that it is not too much of a stretch to think that coding will eventually become the Latin and Greek of our culture.
Huh. I'm not sure even how to begin responding to this. The reason Latin and Greek were taught in schools commonly until the mid-20th century is because they not only served as a common communication system in many fields, were the basis of many modern languages, and were the most common languages of historical documents over a span of more than 2000 years, but also were the foundation of much of Western culture and political systems. There's still a vast amount of classical, medieval, and early modern literature unavailable in translation -- and when I saw "literature" I mean all documents, including scientific and technical advances, as well as cultural artifacts.
While I'm not arguing for a return to Latin or Greek requirements, I don't think it's a coincidence that the U.S. government started wildly straying from the original restrictions on federal power in the early to mid 20th century as knowledge of Latin/Greek and related Roman/Greek history (and political science) decreased. Sure, it's possible to read about these things in English in translation, but the widespread use of Latin led to a promotion of related cultural knowledge (see above), including political and philosophical questions. The Founders of the U.S. all knew their history very well and designed our government in various ways to prevent recurrence of problems that happened in ancient societies. All of this is largely forgotten these days, at best a marginal sidenote to history courses in many public school curricula.
And that's just the tip of the iceberg. Latin and Greek had even more benefits for learning about English language -- both in contrast and through the systematization learned through formal grammar classification. And the etymological aid is significant in deciphering a lot of technical English words.
In fact, the entire system of rational discourse itself has suffered greatly with the decline of Latin and Greek study. Not because these language hold any special value in themselves, but we lost of a lot of the accompanying "culture" of these languages. For example, 3rd-year or so Latin students traditionally would study the rhetoric of Cicero, and in the process, they themselves would learn rhetorical terminology. Similar students in Greek classes would read philosophical texts. Whether or not the students continued to read in the original languages, culturally they were imbued with the knowledge and interest to head to Plato and Aristotle, etc. In studying rhetorical and philosophical forms, they'd also learn errors of logic, as well as examples of fallacies for rhetorical purpose.
All of those qualities would be important for people to know today as they are confronting political speeches and oratory, trying to parse their persuasive style and rhetoric, their methods of "stirring hearts" and their fallacies glossed over.
Obviously back when Latin and Greek were standard high-school curricula (with all of the accompanying classical history, rhetoric, etc.), it was also a different time when high-school was still mostly something done by upper-class folks and those headed in that direction. So whether that would have ever translated well to the broader audience of today's educational systems is questionable. But we didn't really try... we just dropped it.
Finally, I'd just note that anyone who viewed the possibility of reading a Latin sentence as an "intellectual puzzle" doesn't actually know how to read Latin. Latin was basically a living language until the early 1800s among most intellectuals, who spoke it at schools. It gradually died out over the 1800s and early 1900s, earlier in the U.S. than in many European curricula. Already in the late 1800s you can begin to see articles angry about the loss of oral/aural knowledge and how it impeded an understanding of Latin in curricula. The idea of Latin as "intellectual puzzle" is only the horrid end of a dying language tradition as it hung around for several decades after proper oral instruction ceased. Nevertheless, even in this moribund state, it still could lead to many of the linguistic and cultural benefits I mentioned above.
Again, none of this is an argument against coding. But the idea that coding would have the same cultural place as Latin and Greek just seems a bizarre claim.