I'd love for the same to be true of the local church family. It's not that there isn't leadership or authority but that it is not the focus, or the first thing people notice. Hierarchy is never invisible and is an inappropriate structure for family, including the church family. Apart from inevitably working against the servant nature, the 'power under' dynamic of the different kingdom, it ultimately stifles the life and freedom that is the birthright of every child of God. And it requires constant attention to maintain - over the years I have heard more arguments about and attempts to organise how such church government works. Family is far more organic and vital - it also requires continual attention, but this is to all of the relationships involved, not just to governmental structures.
For the church to work effectively as family, we need to prioritise relationship, release the gifting of all in the family, including the various gifts of leadership, and discover those spiritual parents whose gift, maturity, faithfulness and stability help bring strength and security to the family even as other kinds of leaders are released in their gifting.