It's hard for me to imagine the government being simultaneously too incompetent to spend tax money sensibly but competent enough to direct an effective lottery

It's hard for me to imagine the government being simultaneously too incompetent to spend tax money sensibly but competent enough to direct an effective lottery based affordable housing program. If you suppose that the government can't spend taxes wisely, then you seemingly must also suppose that any alternative affordable housing program would be run into the ground by the same incompetents.