This is a Jewish country, and really all of the schools should be run according to the Torah. At the very least, the Torah community should be able to educate their kids the way they desire. It should be the Frum people determining how the secular schools are run (in terms of religious issues such as teaching Torah from a Torah perspective, etc). If that is not going to happen, at the very least, it should be the Gedolim who determine how the Frum schools are run and not the government (at the very least when it comes to Religious issues).
I completely agree, which is why they should not be taking money from the secular government that disagrees with your points.
If all of the Charaidim would be sending to private schools then we wouldn’t be having this discussion.