School influences a child for 10 to 12 hours.
You forgot that school influences begin at the bus stop and ends when after school activities are over, all homework is finished, and all social interaction with school friends ceases.
So...A child sleeps 9 to 10 hours a day. If adults need time alone then so do children. If an adult enjoys relaxing with the Internet and a TV program then so do children. Children also need time outside to exercise and play.
The actual time that a parent can spend to “deprogram” and influence a child is dwarfed by the MASSIVE amount of time that school impacts his life.
First, you would have to have the need to "deprogram" your child. Since my wife and I spent quality time with our children from birth to school age, and then kept up with them all throughout their school careers, there was little need to "deprogram" them from whatever SOME of their teachers inculcated them with. Second, if a parent of a public school student does not put in the time up front (birth on), then it is on the parent for how their child turns out. We raised four. They attended public schools all throughout their educational careers. All four of them vote conservative. Placing blame just on one institution is the same tired type of argument that the anti-gun people are using in fighting for taking away gun rights. The responsibility always has, and should always land on the parent. And, if the parent feels that the school their child is in does such a poor job of educating their child, then they have the responsibility for changing those circumstances.