With respect and without an exact idea of what you mean, they are separate environments. As such, the parallel rules idea is nonsense. It serves no purpose to destroy the home or other environments in order to reinforce school structures. Further, schools have made a lot of policy errors in regards to how they handle children and what rules they use. You'd have that mimicked at home?

At school children are expected to stay in their seats. I don't want that at home for my kid, except at the dinner table. I want her up and moving, exploring.

Kids have to walk down the halls at school with their hands behind their backs. I don't want that at home. It looks ridiculous. I want her to practice walking and running normally without flaying around all over thr place.

Kids aren't allowed to speak at school without raising their hands first. I don't want that at home either. I want my kid to feel it's safe and desires that she come talk to me. About anything. Any time. Obviously, there are some boundaries there, but they're different at home than at school. As they should be.

I could go on. But you get the idea. Different environment. Different rules.

Kids aren't so stupid that they can't grasp that they are required to behave differently at school, at home, at church, out playing with their friends, as a guest in someone else's house, in public, at the library, at an arena, on the ballfield, etc.

There's overlap, sure but the rules are different in varying degrees everywhere.