Why isn't the DoD and the DoHS the same thing? Because you don't want the cops to also be the military. You should spend some time reading up on history to find out why. And what specific form of government really really loves having the military do the policing.
And private schools are better? No, they're not. Private schools have a smaller student population and thus have a better student to teacher ratio. Public schools, when they have the same student to teacher ratio, have the same results.
Now, what's the average cost of a private school in the States? It's $12k a year for elementary and $15K a year for high school.
What's the median income for 1 person in the US? It's roughly $37K.
So, you can see the problem right there. But you're probably thinking, "Oh, well, because they don't have to pay taxes for public schools, they can use that money to cover tuition!"
We pay just under 4% of our annual salaries for public school funding. Do you think 4% of $37K covers that $12K? Does it even put a dent in that amount?
So, what is a parent to do? Enter student loans. Do some quick math on 8 years of $12K a year and then 4 years at $15K. That's $156,000 just to complete high school.
Imagine being 18 and already being in the hole for $156,000. Buying a car? Saving up to buy a house? AHAHAHAHAHAHAHAHAHHAAHAHA.
Don't think that will happen? Just look at the public universities. They did it there. They'll for sure do it to the elementary, junior/middle schools, and the high schools.
Hey, maybe you went to private school and they didn't teach you about the 'Company Towns.' That would be some good reading for you so you can learn what it was like when the company you worked for owned your house, the grocery store, and the school your kids were going to.