Like your quote about the $12,000 per student, it is a half truth.
Statistically, the average depth of the Mississippi River is only 5 feet, however, if you try to walk across because you are 6 feet tall ... you will drown. That is because the average depth IS 5 feet, but some parts are less deep and some parts are MUCH deeper. So too with the average of $12,000 per student. Many students cost far less to educate because the cost of the classroom and teacher is divided among 20 or 30 students. A Third Grade teacher with 20 students (a small class size) does not earn $240,000 per year ($12,000 x 20). However a legally blind student with 10% visual acuity might require a teacher's aid to assist them, and only them ($40,000 per year for 1 student).
Here in Florida, we have 3 ways to attend "Public School" (Plus the option to Home school or private/charter school). You can attend classes at a brick and mortar school (when they reopen), you can attend classes remotely via a "skype" virtual classroom, or you can take 100% on-line e-school. My high achiever daughter has done all three and WANTS to return to brick and mortar school to see her friends. She actually did best in e-school by finishing two years work in one year and a summer.
What about children with learning disabilities that need special instruction. What about children with emotional/behavioral issues. These are the ones that cost the most to educate. Are we prepared to dump them on the street with no education because we defunded the schools that had the resources and expertise to deal with them?
What you are actually proposing is to do to Education, what we have done to Mental Heath. Save money on treatment and deal with the mess down the road. There is no need for Public School ... except for the children that really do NEED it.