Another popular bilingual immersion option is English-Mandarin. I know people here in San Francisco who have kids doing bilingual Mandarin immersion, apparently with good results. I love Latin and Latin teaching, support its availability, and think it's benefited me and other students who were given the opportunity to learn Latin, but I think you're right that the recent modern-language immersion trend is incredibly valuable and deserving of support. We should want language teaching to be effective and beneficial for students.

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.