It sounds logical but guess what: it’s not working. Ask any school administrator anywhere in the country if there is a shortage from both Male and Female teachers.
Secondly your suggestion of hiring cheap labor means that you will get what you pay for. Perhaps in a factory in China it pays to hires unskilled labor to install widgets but if you wanted dedicated professionals to teach your kids and grandkids it will cost.
This leaves only two sources for the money, philanthropists, higher tuitions or both.