This is potentially a good idea, a bad idea and a difficult idea.
You have laid out how and how it might be a good idea. No need to rehash that.
It could be a bad idea because Philosopy is the pursuit of truth. Truths are often inconvenient. Public schools are hardly hotbeds of free thought. Any truth determined dangerous will be suppressed, making the whole program useless.
It would be hard to implement because it would require well educated teachers. Most teachers in the last 30 years have had weak educations and are poorly read and quasi literate themselves. Ideology has replaced philosophy in most colleges. Where will this cadre of new, educated teachers come from? Fewer and fewer young people want to be teachers. Enrollments in teacher education programs are down across the nation.
So again, I like this idea, but think it unlikely and untenable.