These days we have good models for how to teach bilingualism to kids: dual-language immersion schools, in which both languages are used extensively in coursework. The problem is that this labor-intensive model will be impractical outside metropolitan areas with school choice, or communities with a strong heritage language community.
Latin may not be a living language, but it remains very widely used in scientific terminology, law, religion, and elsewhere. Like the prestigious national languages, it is a mark of erudition and social status; the demonstration of which is itself a purpose of education.
A superficial literary understanding of Latin gives you middle class bragging rights and a substantial step towards being able to parse the original text of a literature which has been exhaustively translated into English, complete with notes on shades of meaning. (And an even more limited grasp of some of the fundamentals of Spanish, I suppose) And since the source material is all ancient texts, you can't even pep the teaching up with some relevant and modern material or motivate the students by the prospect they can use it to backpack in Peru or do language exchange in Madrid.
I'm not persuaded that the inadequacy of languages teaching is an argument for the same time to be devoted to devoted to something which is even further removed from being useful and the teacher is even less likely to be adequately equipped to teach.