HomeSchooling goes K-12; in addition, most homeschooling courses are sufficiently flexible to easily allow "dropping into" a Religious or Private School and/or "dropping out" into Homeschooling therefrom (I speak from familial, albeit not personal, experience). Homeschooling courses do not, however, usually integrate as easily with Publik Skooling... too much "culture shock" and disparity in Educational Quality.
If so that is feasable but many parents do not have the education themselves for home schooling much less the time or devotion to do it.
Combined Federal, State, and Local spending on Publik Skooling amounts to over $7,000 per-child, per-year... and with the passage of the Kennedy/BushJunior "education" bill, expect the pig-trough to get even fatter.
Just return that money directly to the parents via the abolition of the Property, Sales, and Income Taxes which support Publik Skooling. If you want to do so in a manner which "helps" the poor, you can abolish the Sales Taxes first... oh, and abolish State Lotteries also, which amount to a "tax" on the Poor to subsidize Middle Class schools.
A fairly-high-grade (substantially better than Publik Skool, anyway) Private Religious Academy education in a Classical format (Greek, Latin, Logic and Rhetoric included in the basic curriculum) can be had for 60-70% the cost of Publik Skooling... $350 to $400 per month -- again, I speak from familial experience on the matter. Just give Parents back their money; those that have the time and ability to Home-School may keep the cash, those who lack the time and ability to Home-School may spend less money on a better Private/Religious product.
That being said, there is a real need for competition with the public school system and that will come only with some type of voucher system. Absent that there needs to be the political will to shut down schools that serve as indoctrination centers and warehouses.
Yes, the Political Will is grossly lacking at this time.