If you want to think outside the square you have to get out of the box.
Lately I have heard so many people complaining about the school system and how it failing the children. Pet complaints seem to revolve around schools not teaching enough real world common sense, not enforcing enough rules around common decency or manners and lastly not catering enough to different children and their learning needs. Many people feel that the system is faulty. But what they are really finding is that mass education has been designed with round holes and they are square pegs. They have also failed to see formal schooling for what it is and what it is designed to achieve.
Compulsory schooling is designed to keep children occupied while their parents work. It is designed to keep them out of trouble and get them accustomed to living in a highly institutionalised world while instilling a set of values that is desirable in a conformist and cooperative society. Reading, writing and arithmetic are important but so is learning to do what you're told, when you're told, how you're told. These attributes make good employees and citizens.
So unfortunately if you are wanting your children to be educated in a certain way and about stuff that hasn't been deemed important than you are going to have to think outside the square - In fact you have get out of the square. Move away from mass produced, bulk delivered lessons and start putting in the energy to educate your child yourself. This isn't illegal. There are many options for homeschooling and lots of resources and support to help this process but it is going to take work, time and dedication. So if you are not willing to put in the hard effort and want to receive free education with little parental effort be prepared to receive what the institution decides.