Some do, some don't. That's just how things are. It is incumbent upon those who lead to incorporate that vision for posterity and to teach. Too often, whether it is business, government, or religion, fathers spend so much time on their work that they forget their first responsibility to both home and community, relying upon distracted institutions to pass the baton. It's the tyranny of the urgent in the pursuit of status and wealth.
Even in good times only a small minority of God centered people exist; in bad times, only a few.
That is not my observation. It would seem that in bad times people tend to remember the Lord. Consider the behavior of the children of Israel in both sets of Kings and Chronicles.
Obedience to social heirarchy need not violate justice unduly, and can make bad times survivable.
Or it can make them worse. It depends too much upon the despot. I prefer the Republic to hereditary nobility. Without the hope of the individual for a leap out of their current status, the entire society loses hope, much as we see in socialist dictatorships, where the hierarchy is to government or a rather less than benevolent despot.
If your community consists of serious Christians now, there is no guarantee about future generations. And those serious Christians will certainly sort themselves out into a heirarchy, and try to pass on social position to their offspring.
I don't worry about passing on hierarchy or social status to my children, I focus upon their education, both temporal and spiritual. I homeschool both my kids and incorporate them into my business life as much as possible, not as a way to pass on an advantage over others, but because I think it will improve their education.
I believe I agree with your point of view except (and I am no Calvinist) I believe mankind too fallen, too sinful and half witted - certainly including myself in times past - to live in peace without a respect for authority. A good father (I pray for the grace to be one) will raise children that respect him and themselves. Such children will render Caesar what is Caesar's, without illusions, without guile, and without servility.