In the recent Thor comics, after losing Mjolnir, he also loses his arm to Malekith. Odin calls upon a dwarf to forge him a new arm, composed of Uru. But...why? Odin is a reality warping skyfather who has destroyed galaxies, revived the dead, and created planets from nothing. Why not simply heal Thor, regrowing his arm. If he wanted Thor to have a magical Uru arm for some reason, he should have been able to create that as well. So, beyond PIS, is there any reason Odin couldn't simply will Thor to be healed?
The answer is: Because he didn't want to. Yes, Odin is completely capable of growing the Odinson a new arm, if he so desired. He didn't. He preferred to let Thor be without one, as with so many things between those two, as a lesson to be learned.
The relationship between the Odinson and his father has always been a complex one. With Asgard in flux, no longer in its own private dimension, threats to Earth abounding and Asgard not in peak performance, Odin has a lot on his plate. Add to that, a mysterious woman (who granted, to Odin, MAY not be the mystery it is to the rest of us, and woe be unto to anyone if it IS a mystery) suddenly becoming worthy enough to wield one of the mightiest weapons in his kingdom and you have an All-father who is truly peeved.
Currently The Odinson is not in favor with Odin. He has lost access to Mjolnir. In and of itself a statement so great, there is little left to be said between them. He, however need not be without the resource and since he can have a new arm made for Thor, he does. Keeps his craftsmen happy and resolves the issue of his main enforcer and protector of Asgard, being fully armed...so to speak. He all but says so below:
Eventually, as with all things, Odin will either allow the Odinson to correct his own problem or if he should become worthy enough to wield Mjolnir again, grant him access to either magic or technology which will give him a functioning arm, once again.
You have to realize, Odin doesn't like correcting the Odinson's mistakes. Remember, when Thor was banned from dying by Hela, and cursed with brittle bones, his body became a mess held together only by armor? (Thor #373) Odin could have fixed this. He did not. It's not his way to fully correct his son's difficulties unless it suits his purpose to do so.
As a side note: Odin's eye is lost as a sacrifice to the Well, Mimir in exchange for knowledge of previous Asgards and previous attempts to avoid Ragnarok, the Twilight of the Norse gods. As a sacrifice, the eye can never be regrown. It was the price of knowledge.
A second side note: Tyr's hand was also lost as part of a sacrifice to bind the Fenris Wolf. It will also not regrow due to the nature of the sacrifice/betrayal necessary to place an unbreakable chain on the wolf. Odin isn't being cruel to Tyr. It was his destiny to sacrifice his hand for the benefit of Asgard.