(Quick replies. See the underlined note at the end)
Why is cloak slot crucial?
To complement Gaxx + Claw of the Kazgaroth with the Cloak of Protection +2. I typically play with non-shorties to avoid trivializing the game with early access to highly negative saves. The Gaxx + Claw of the Kazgaroth + Cloak of Protection combination allows non-shorties to make their saves after a dispel. Malisons just have to be countered with a potion.
I don't know how can it "cancel" Haste.. I doubt it would cancel your haste once you put it on.
It does. And that's how Free Action should work in my opinion. I like that dynamic.
Well, I haven't seen Tamah/Asc in a while (grrrr....
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Her breath weapon applies the sleep effect with no save offered. Eleven racial bonuses won't stop it. The Greenstone Amulet is the only way that many characters can foil it. The times I've lost that fight it has been because of sleep. Remove->Sleep in particular. With an undispellable Greenstone Amulet, that problem is solved.
But in my game, there are no less than *5* exellent amulets.
As mentioned earlier, context matters. I'm speaking within the context of my install and playing style. I can't comment on the balancing of IR items within the IR context. I've never attempted to do so.
I don't know how a battle vs 2 dragons + drakes can be made trivial, Ascension even less so. Then again, I haven't fought these in ages. 
I've soloed the Ascension battle many times with many classes. Undispellable Greenstone Amulet + Reflection Shield + Movement Rate advantage + Elemental Resistances would basically solve it. Using a variant of that approach, I've soloed it with a beastmaster and an unkitted cleric amongst others. Aside from Mel's Bone Blades at the end, the crux of the challenge was protecting against Implosion Hold and Power Word: Stun without nerfing the movement rate or clouding aura at a time when it might be needed to counter a Mel Time Stop. A permanent undispellable Greenstone Amulet would take care of that.
Unless you have uber-low saves (which in most cases nullify Greenstone use anyway apart PW:Stun), you won't be safe.
Now you're getting it. Using potions, items and spells, I can always make my saves. The only real threat throughout much of BG2 for my characters is PW:S. For many characters, the only way to stop it in my install without nerfing movement rate are the Sword of Arvoreen and the Greenstone Amulet. Arvoreen is only available to halfling and UAI rogues. The vanilla Greenstone Amulet is in the Underdark and its limited duration, dispellability, and activation delay limit its utility. An undispellable Greenstone Amulet in the Chateau would take care of that threat.
Rayic has a random kit with random spellbook - unlike some other mages, he doesn't always have a specific kit (Lavok is always a Necromancer, Jon is a Conjurer etc.). Until Grond0 meets him for the first time, he has no way of knowing other than an editor which shall it be. If he's an Invoker or Necromancer, Greenstone will do jack s***, since Rayic could easilly kill him with sequencered Skull traps/Fireballs or FoD.
I can't comment on Grond0, but I can comment on how those situations play out in my games. Basically, they're not an issue. I fight mages at range and maintain a clear aura, which allows me to put counters in play before spell effects hit. I collect a comprehensive potion collection early in the game, and then drink the one I need the moment I need it. Power Word: Stun is the biggest threat by far, since it casts fast, grants no counter window, and doesn't offer a save. When mage battles become dangerous, its typically when hitpoints get low enough to bring Power Word: Stun into play and there are pursuing demons on the field. In that situation, equipping a Free Action item would slow me down, making me vulnerable to the demon. An undispellable Greenstone Amulet would solve that problem while freeing me to use my aura for another counter.
The BoIB + negative save +(or Potion of Magic Shielding, if necessary) stops Skull Trap sequencers. The Reflection Shield stops Flame Arrow sequencers. FoD offers a save. I've never had problems with those.
Be that as it may - it's probably a much more powerful item when you're soloing then playing with a party.
It is more powerful when solo. But in the context of my install and playing style it goes beyond that. There is a small number of things that are actually a threat and an undispellable Greenstone Amulet solves or simplifies those problems. It basically fills the last holes in the defenses and that's what would make it unbalancing in my game. Additionally, it would simplify the task of taking care of the other manageable threats by freeing up cognitive bandwith. If I didn't have to worry about my disabler defenses -and didn't have to worry about my disabler defenses being dispelled- then all I'd have to do is focus on my movement and elemental resistances. Most of the crucial game decisions I face would be solved or substantially simplified by having that item.
Again, it differs from player to player. For others the item would be insignificant, in the context of my playing style it would be a huge deal to have that item in the Chateau. I can't comment on how it would play out in your install with your playing style.
I think we can put this to rest. I take your word for it that you don't find it unbalancing in the context of your playing style and in your install. You should take my word for it that I would find it seriously unbalancing in the context of my playing style and in my install. We should all do whatever we like. I don't think there's much more to say. It was fun talking to you though Aasim!
Best,
A.