The first time Laufey tried to kill him with an icicle was on Jotunheim when he came to rescue Thor and the gang. Allfather was looking "tired" but he was not in Odinsleep.
One thing I wondered about, and this may be my Loki fangirl talking, but hear me out. I mean, it's sort of disappointing to me that it's a supposedly very advanced civilization and all they can do for a person who has basically had an emotional/mental breakdown and commits crimes is throw them in prison and toss away the key (it would seem). So I wondered if Odin trying to use his power to straighten Loki out, and that could be part of his distraction at first. MCU Odin cares A LOT more about Loki than Comics Odin, and he blames himself for Loki's behavior to some extent I'm sure, so I find it hard to believe he wouldn't want to try to find a way to repair the damage if that's possible.
For instance, I'm also not entirely sure that it won't be revealed that the staff/tesseract did have an effect over Loki during the time of Avengers and so Odin may have to deal with helping him get that out of his system (not that Loki still doesn't have issues!). Per the deleted scene Loki says "It effects everyone differently." I've previously wondered if it could be exacerbating Loki's fragile and very angry mental state. Clearly Odin's two ravens were there, watching the conversation between Loki and Thor for a reason, and it may have revealed to Odin how or why Loki's mental state had deteriorated so much (so much that he was lying to himself about what had happened back on Asgard). And Thor asks "who controls the would be king" indicating that he thinks Loki is being controlled by someone or something. This may be more of a hope, than what will happen, admittedly.
However, to read the Italian film clip summary, it makes Loki seem pretty out of his mind, and he's not going to go along and help Thor, or be much help to him if he did, if he's like that. Not to mention he'd be a serious danger to Jane and so not too smart of Thor to go on a trek with both of them. So I think that something needs to stabilize him at least some, I'd think and I'm not so sure that just a hug and a talk from Frigga will do it. Tony didn't mention having scenes with Tom, but they have been pretty mum about Loki, and certainly after what happen in Thor 1, I can't believe they would not have at least 1 scene, if not a story arc of their own to be continued. And if Odin finds he needs to mess with the Tesseract in order to free Loki of it, then that could be a legitimate reason why he is distracted/unable to do much during this time, while he does battle with that power (and I mean in more of an other world battle of the mind than a physical battle). So maybe he frees Loki of it, but still has to battle that power, even after, or is sent out of commission for a time from that battle. Then Thor becomes King in the interim. And maybe during the course of Odin's battle, the presence in the Tesseract is freed and turns Algrim to Kurse. It would also make much more sense for why Thor would give Loki yet another chance to work with him and potentially redeem himself, if he believed that the Tesseract was effecting him during Avengers and now he is free of it.
I bet Tony didn't realize that was a possibility when he signed up for the role. LOL Poor guy has a lot of trouble getting around with the eye patch on, I'm not sure how well he'd do acting all that out. LOL
And as mentioned above, if it's determined to have an effect or hold over Loki then that may give Odin a good reason to be messing with it, and not just lock it away for safe keeping.
and I think the most powerful being in the 9 realms line is in the deleted scene, no? So not necessarily MCU canon, but I do understand he should be that (otherwise he would not be king!)