This applies more towards the original SNES versions than later ports of the game. However, the fundamental problem is self evident...
The Cursed Ring had been a legend that evolved from tales of discontent or mystery.
For instance, it was rumored that it unlocked some hidden secret of Dark Knight Cecil.
Then again, it was also rumored that it did... literally nothing, outside of the poor stat loss.
The only thing "cursed" about this piece of armor... it did something, but it's actually putrid crap.
The sole purpose of the Cursed Ring is to simply upgrade "resistance" to absorption.
On paper, that sounds like a great idea, considering bosses and the like use a lot of elemental attacks to deliver damage.
However, this came at a measurable expense... crippling the character... both physically and magically.
In FF4, the amount of magic damage you take is simply knowing how powerful a spell is through the spell multiplier (monster's magic stat/4) vs the character/targets's magic evasion multiplier (a combination of Agility/32 + (Intelligence+Spirit/32) and the magic evasion stat. Simply put, Rydia is #1 in magic evasion, vs Yang is #1 in taking magic damage (especially with his special charging attack command).
Absorption relies on actually
taking the most magic damage that you can, so crippling Agility, Intelligence, and Spirit accomplishes that... decreasing Strength and Stamina is superfluous. Although, losing strength is generally "fair compensation" for this benefit, but lowering Stamina is generally pointless.. since the armor accomplishes that by its lack of evasion. (Whatever, 7 points of defense is nothing to cry over).
The Cursed Ring relies on armor to take the benefits of this feature. This armor is limited to the elemental armor sets... Fire/Ice Shield and Armor.. the Diamond Armor sets, Protect Ring, Crystal Helm, Dragon Armor set, and FF4A's Red "Burning" Bard set and the Cat Hood (with honorable mentions to Vishnu Vest, Rainbow Robe, Caesar's Plate, Dragoon Plate, Robe of Lords).
On the surface, this would most benefit a fighter type character... since the Cursed Ring will simply cripple Tellah out of existence. most of the original game's elemental resistance resides on the Protect Ring, thus limiting elemental benefits to generally Cecil and Kain.
However... taking advantage of this in a general sense... is pretty... horrific.
Consider what monsters actually used elemental magic. There are two specific types of damage magic that are used...
1) Damage magic - Rubicante's Glare (Flame Dragon/Tornado) is the most notable elemental attack (Fire). This would usually be the most opportune time to use the ring, right?
Wrong. For as many characters that would make this a usable option (1 in 5 chance... 2 in 5 chance if you luckily get two of them), he will still end up obliterating the others with that spell just because he can. So if you spent all that time collecting elemental resistance... well, he's the only memorable choice.
Note that most monsters do NOT use such magic. Unless you are stupid enough to play with the Tricker monster, you will rarely find any regular monster or formation that uses strong elemental magic... and at best you would consider the Red Dragon... but that's an easy monster to beat the crap out of. Anyways, most monsters fall into the next category...
2) Damage based on target's HP + elemental - The first time such an attack is applied to you is from the Dark Dragon... yes, the other version of the Dark Elf. Of course, you didn't have resistance to Fire yet (and it looks like an ice attack too... kinda like the IcyBlaze attack). Then you eventually meet the IceBeast that attacks based on the monster's HP... and then the finally the FlameDog chest (containing the Fire Sword) teaches you why equipping the Fire Armor early was a "totally horrible idea" (tm)... though that's generally a non-issue later. You would eventually encounter FlameDogs and Chimeras combos... which can potentially murder you while alone....
Then, you find out that the healing you gain from this... is pitiful. The algorithm that derives healing from damage spells uses the algo for targeted HP spells. It uses same fractional number that the HP-target spell to calculate damage. So, for the FlameDog's Fire, it's 5 (because it normally would take 1/5 of your HP if not resistant to Fire), and the Chimera's IcyBlaze is 4 (it would take 1/4 of your HP if not resistant to Ice). In sum, you get a pity healing.
It's actually worse when combined with the Adamant Armor.. despite negating the bad effects of the Cursed Ring, Immune takes precedence over Absorption.
I guess that's an improvement in FF4A (and probably WSC as well, in addition to the later ports). The healing done by point #2 is based on the monster's HP, which I guess is a plus, but that also means that hurting the monster also hurts your healing. Then again, ZeromusEG and the Brachioraidos fuck thus up badly (the Hero Shield being part of that problem) and now it's a complete and total clusterfuck (like, getting healed 9999 type of imbalance).
The Adamant Armor in FF4A suck far less.. since Absorption takes precedence over Immunity...
So, if you ask me now if the Fire Scarf in FF4:TAY is imbalanced... now you know why.

Forgot to mention Gold Hairband and Light Robe into the elemental armor mix.