The other thread is getting quite crowded and with a steadily clicking clock, I thought I'd create a separate thread. It's taken some time for me to best articulate why I think the Amulet Crown is problematic:
[First Order Effects]
#1. Giving up the head slot isn't actually a big sacrifice
The main argument that the Amulet Crown is balanced, seems to be that the player is giving up some Might sets. But this makes several major assumptions: namely that players with the Amulet Crown have a lot of Ultra Rares (and have a large enough collection for a 3-piece or 5-piece set). Many players don't have a ridiculous number of ultra-rares, in which case giving up the head slot is really an easy decision.
Let's look at the head items:
Great Helm / Cassis / Elven Coif / Triton Helm
Helm of Clear Thought
Helm of the Boar
Helm of the Eagle
Only the Barbarian / Cleric / Fighter / Paladin are actually giving up something substantial (+1 AC) in most cases.
Cap of the Owl
Catspaw Hat
Hat of Escape
Any class can use these but none of them are particularly impressive.
Mithral Cap
Dragonscale Helm
Helm of Retribution
*If* you have one of these Ultra-Rares, then the Bard (Mithral Cap), Druid (Dragonscale Helm), or Ranger (Mithral Cap or Helm of Retribution) is actually giving up something.
Crown of Might
Hat of Healing
Hat of Healing is quite weak. Crown of Might is the best argument but that's only if you have that particular Ultra Rare.
Circlet of Elemental Mastery
Coronet of the Arch-Druid
You can always put on the Coronet later on in the dungeon when you need it, so no loss there. Circlet of Elemental Mastery is trickier because it's a nice effect for the Wizard. But honestly, it often isn't needed in a dungeon and at most, it'll help with one, maybe two spells. So it's not as helpful as most Amulets would otherwise be.
For 6 of the 10 classes, giving up the Head slot is trivial if you don't have any Ultra-Rares. For the other 4 classes, giving up the Head slot can still give you a net 1 or 2 AC bump if you use the Torc of Natural Armor or Oakskin Medallion.
Even if you have Ultra-Rares, the AC from Torc / Oakskin is still better than the AC you could get otherwise (for the Bard, Monk, Rogue, Wizard). If you want to go with a different Amulet, it's still an easy decision.
Even the remaining classes (Barbarian, Cleric, Druid, Fighter, Paladin, Ranger) can get a slight bump by going with the +3 AC Oakskin. Giving up the headslot for a non-AC amulet (Horn of Plenty, Amulet of Wonder) is a slightly bigger tradeoff since they lose a +2 AC Helm.
The Crown of Might may be a legitimate argument for all classes but I think most amulets are probably more helpful. Plus, if you want to get technical, the Necklace of the Oak is actually superior to the Crown of Might. It gives the same bonuses to melee weapons, plus it helps with Mighty ranged weapons as well.
#2. Set bonuses aren't a significant problem
Mithral set is a non-issue. The 3-piece set is conditional (breath weapons. How often do we see that?) and the 5-piece set is conditional (anti-undead bane. You can easily miss this). You can still make the Mithral 3-piece set pretty easily with Armor / Gauntlets / Boots, and possibly Sword. So giving up the Mithral Cap is quite easy.
The 3-piece Might set is easily achievable without the Crown. In fact, it looks like most players are going with the Scepter / Girdle / Boots approach. It only becomes a sacrifice if you're going for the 5-piece set (which requires 5 Ultra-Rares and involves only a small portion of players).
The Dragonscale set has less flexibility so you are giving up 8 points worth of fire reduction (10 - 2 = 8). That might be harder in some cases. But if you know the dungeon has little to no fire (you know which monsters you will face or say, a certain underwater adventure?) then it's not much of a trade off at all.
#3. Amulet choices are strong
The following are non-issues because they're relatively corner-case are limited in power:
Amulet of Mugwort
Necklace of the Elm
Necklace of the Bay
Amulet of Thorns
+1 Amulet of Armor
Necklace of the Ash
Harpy Claw Amulet
Necklace of the Oak
Scarab Amulet thingy
Hand of Glory (amulets are generally better than rings)
Necklace of Fireballs
Periapt of Proof Against Poison
The cases where the Amulets are extremely powerful are:
Amulet of Wonder
Horn of Plenty
Medallion of Greyhawk
Dragon Tooth Amulet
Torc of Natural Armor
Barkskin Medallion
HoP and AoW have traditionally been viewed as the most powerful tokens in the game.
Torc and Barksin contribute to AC creep (especially when you can combine them)
Greyhawk and Dragon Tooth can be actually quite good - protecting you from a wide variety of effects.