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I've been playing a lot of ARAM recently, as I don't really like the normal game and coop isn't doing it for me anymore...
I have to say I don't really see any overly powerful items in ARAM in S3. Warmogs used to be the saving grace for a full bruiser team, but stacking those is kinda moot now. You would be better off with a multitude of high health items rather then just one, like a warmog and a frozen mallet. It really doesn't make sense to stack mogs now.
Honestly though, the chalice might be too strong. I think that sorta applies in general though, in all the game modes I've played it's sorta the one stop answer to mana problems. Although that's a good thing and you have to spend money to build it, perhaps the alternatives (such as Guardian staff) aren't good enough. Perhaps making the mana build faster per cast or tweaking the return on AP above a certain threshold. If a chalice was removed you'd see AD carries raping everything... At least AP can sorta fend them off till they get fed. AP would be rather worthless too as you burn through a lot of mana really fast in ARAM.
AD carries get ridiculous quite fast, but that's normal.
Some items definitely could be buffed to be helpful, but I don't think any nerfs are really in order.