Do you have a spouse? You might be worried about public school quality, but at some point it would be cheaper to just have the spouse stay at home and home school.
And why do you think having a full-time tutor is cheaper than group care at a school?
As to why it's cheaper, that's a calculation they have to make. If the spouse's net income (looking at marginal tax rates) is greater than 3k a month, then it's not cheaper.
You seem to imply that “anyone” can be an effective teacher. That’s simply not true. Plus many children react much better to people outside the house. I was definitely that way. And my wife has many amazing qualities but she would make a horrendous teacher.