Ok, it's not just bureaucracy, because the mistakes that AI makes to favor efficiency are different than those made by a large chain of overworked and sometimes corrupt people. But the root issue is not AI, it's the badly-implemented policies that the AI is designed to carry out. Look at any other strained system (food stamps, DHS, IRS, not government but Google and Amazon customer support), we have real humans carrying out bad policies and it's not much better.
Most people really do have morals and don't like hurting others, but those morals only go so far when you're part of an underfunded system, apathetic from burnout, and you literally don't have the resources or ability to make the morally-correct choice. All this debate on how AI lacks empathy and common sense place way too much value on humans who also lack empathy and common sense, and while an AI programmed to do something unethical won't hesitate, history and experiments show that some humans won't either.
We definitely should be learning and understanding the limits of AI and its hold on ethics, and not delegate policies like laws and income to 100% automated systems. But AI and improved efficiency really can help a lot of government institutions. Especially when the AI takes over the mundane, and the people in charge can handle the more difficult cases. Because then those people can spend more of their "human" empathy and decision-making better.