This seems extremely problematic to me. If we can’t question or judge the motives and actions of an authority, even one infinitely greater than ourselves in every regard, then on what possible rational basis could we believe that authority to be good? I think the comparison you make to earthly authorities is useful, actually. Surely you would not think it wise for humans to obey any government absolutely and without question? Our obedience to and trust in authorities should always be contingent on our independent judgments of those authorities. There are many, many historical (and contemporary) examples of where unquestioning authoritarianism can lead humanity.
I am not suggesting that authority is always harmful or obedience to authority always wrong. I am suggesting that unjustified and unquestioned authority is harmful. This is not even an argument against theism or Christianity. An omnipotent deity might in fact be perfectly good, but how could we know whether he is or not if we decide, a priori, that this entity’s every action and very essence is the definition of goodness? It seems to me that if Christians adopted an essentially secular moral system that pinned moral goodness to human well-being, then we would have a rational basis for belief in a good God! We could observe his actions toward humanity (I’m granting the possibility of divine revelation through personal experience or the history of God’s actions recorded in the Bible) and then come to some conclusion about his character based on how those actions affected the well-being of people. I really, really can’t figure out how this unquestioning obedience stuff can be anything other than damaging to people, both morally and intellectually.