The supposed economic value from learning modern national languages is wildly overstated, for English monolinguals. It's better to learn languages because learning languages is valuable for its own sake, and pick the language you learn simply because you like it.
There is a huge disconnect between our implicit goals for language learning in this country and the effort we expend upon it.
I strongly believe in the value of language education, but given the amount of time and money we're willing to spend on it, we'd get as much or more benefit from making them study Latin.
With Latin, all the people who want to learn a Romance language would get a leg up on it, and all the people who want to study biology would get a leg up on that, and people who are fine with just speaking English will get more insight into their own language.
What's wildly overstated is the benefit learning Latin has on anything other than taking the SAT. Studying French is much more beneficial to speaking French than studying Latin and I shouldn't have to explain why that is the case.
If you buy the critical period hypothesis anyway, which I do not.
The "mandatory one year of foreign language in high school" is a relic of decades past when Latin and Greek were widely taught, and that is what they are mostly what they are suited for. It is just as much a relic as Latin is.
There's nothing on the scale of full-time immersion, nor is there likely to be, but there's now a small minority of Latin teachers who are presenting Latin as a spoken language, including using Latin as the language of instruction and attempting to apply modern language pedagogical techniques like Total Physical Response. So even some Latin teachers might agree with your criticism of the less-holistic teaching styles and the distance they put between students and the language.
Edit: I didn't notice that you were also advocating teaching Latin further up in the thread.
Let's be honest here - nothing of value is lost.
The opportunity costs of even one year of any non-English language for American HS students makes it simply not worth it.