Could the sticking point be that Kytain has never voiced an intention to purchase a home in his wife's name but rather seems to intend to live with his brother-in-law? Perhaps I misunderstood, but Ciambella didn't you state that his wife, My, would not be allowed to be entered in her brother's book?
Of course it is long past time for Vietnam to continue to tie the full privileges of citizenship to the house book. The absurdity of people being registered in distant provinces that they only visit once a year is not reflective of the economic realities of the country in which people move to where the jobs are. The current system was set up for an agrarian society that Vietnam is transitioning away from. If the government wants to keep track of where people are, it would be more accurate to simply record the current reality.