Regarding the reason for Anna's inefficiency, I'm going to sacrilegiously do a cut and paste job on a comment I made to another excellent meta, as it seems relevant.
My own gut instinct was that Anna was unstable, after her torture by her angel captors, and therefore not thinking and operating with flawless logic. Her inefficiency felt to me like that of a maddened and erratic person, or wild animal (angels are forces of nature after all, rather than humans), seeing the world through a warped viewpoint, trying to do a good thing, but handicapped by the symptoms of her trauma.
I think that angels are the agents of fate as long as they are obeying direct orders from God, but since He has 'left the building', they are no longer acting in that capacity, although they certainly believe that they are.
When questions of angels and fate (and free will) arise, my mind keeps going back to a fundamental question.
Why were human beings created? Why did God insist that angels acknowledge them, leading to Lucifer's famous rebellion and the schism in Heaven that is still playing out?
Lucifer points out how flawed humans are: we murder, lie, steal, and trash the planet. Why would God favor these flawed creations and ask his firstborn, the angels, to honor them?
What do humans have that offsets all that potential for destruction and evil?
I think the answer is free will. The ability to learn, and make different choices the next time.
I think that's what the entire theme of the series is about.
It also explains, or suggests, to me, why God left the building.
I think He has stepped aside to let things play out, in the hope (or prescience) that where he has failed by simply ordering them, to teach his firstborn race how to make choices based on what is right, rather than on blindly following orders, that allowing these catastrophic events to occur, perhaps his second born, the humans, in the form of the Winchester boys, might be able to teach by example.
In a way, it parallels the story of Job, if you allow for a lot of artistic leeway. ;) Lucifer was allowed to visit so many awful trials upon Job because God was attempting to demonstrate to Lucifer that his second borns could have faith in the face of it.
Here, they may be the teaching tools to show the angels of Heaven what free will is about, and how choices can be made based on what an individual believes to be right rather than on selfish needs or blind obedience. In Castiel, we may have the single example of the lesson actually taking effect.
Even Lucifer, the rebel angel, is in a way still acting upon a blind obedience, not to God's more recent edicts but to what Lucifer thought God wanted earlier. A pristine world. Complete order.
I agree that Michael, now that we've seen him, maybe smart and awesomely powerful but he is really no better than Lucifer, having no more respect for human beings than his brother. I agree 100% with your take on why he obeyed God's edict - not out of understanding but simply because 'orders is orders'.
Gabriel may actually be in a better position than Michael, or Raphael, to begin to understand what is happening, now, post Changing Channels.
Castiel still seems to be the only one who has learned from what is happening, though that is taking all of his words and actions at complete face value, which may turn out to be a blind.
All of this intellectual stuff aside, this episode killed me dead because of one thing - Sam. There is not enough Oh Sam in the universe to acknowledge his (via Jared) reaction to meeting his parents and I'm so damn glad this happened. I've read a few episode reactions where people have said nothing significant took place in this episode, perhaps aside from Michael's appearance and talk with Dean, but with Sam on the balance of one of the most important choices (Dean being the other), of this entire Apocalypse, every experience he has is significant. The key to Sam unraveling his famous anger may have been in his meeting Mary, and talking with young John.
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Songs in the Key of Supernatural