You made a new paragraph and started the phrase with "was very similar situation", if you're gonna complain about my reading comprehension I can complain about your grammar m8
I suppose blame that on the forum. I hit the spoiler text, input Kyuuem No1, and it just removes the entire name when I posted it.
However regardless, I go from using vague terms to specifically "she", begin talking about multiple different bosses from this game, and reference one that requires shit bombs, something that is unique to Sequel games and not Black Souls, uses dangerous AOE attacks prevented by shit bombs meaning it's a buff based attack, and has 3 health bars. It should be plainly obvious who I'm talking about, Kuuem No1, the finale of the "core" story and what is meant to be the biggest moment worth remembering about the game.
It's like seeing a locked door and I mention kicking it down is the best option, and the idea I'm referencing Rabi flies straight over your head...
None of your points negate what I say either. Idea hits you with forget and blindness, meaning you need to make sure your DPS resists blind, ideally both, and your medic resists forget. That means you can't use equipment because you need to use ailment immunity in those slots, or sacrifice a considerable amount of damage/defense by using weaker armor/weapons that resist those ailments. Kuu can't keep up with the amount of healing required, unless you're using his AOE heal, however since that costs 40 SP and the boss attacks hit you so hard each turn, you're on a timer in terms of how long it can last.
A "puzzle fight" is a fight where the boss is not a test of raw damage, but a fight where there is some gimmick you must understand, and work around. The Old King is one, as it plants a seed inside you that is a guaranteed kill no matter what that can't be survived, but it's only planted due to the attack landing, meaning a dodge will prevent it. As you say yourself, stunning the mirror clones is the solution to the second phase, and it also is required for a few attacks in the first phase as well, and for Muramasa, you need to figure out what combination of buffs and effects enable you to survive the final phase because just blocking and stacking raw defense won't do anything. You can get lucky and happen to do the right thing, but unless you break the entire system the fight is using, the puzzle part of a puzzle boss can't be avoided
A puzzle is still a puzzle, even if you can also just blow the entire thing up to get past it. The ability to brute force something with enough stats doesn't make it no longer a puzzle boss.
In the case of Kludge, Kuuem No1 is a puzzle fight, as her AOE Errorstone attack is absurdly powerful, so the solution is to remove the buff and stop it. The fact she has 3 health bars adds to that, as you can't simply one-shot her to skip past her attacks, she will perform them, and you need to know how to prevent them. Idea is the same, as at least in theory, as she rotates through a strict attack order of powerful moves that require some solution, often being either binding, stunning, or lowering her attack to 0 with Faria.
The problem however is that a 5 attack rotation with 2 of those attacks being absurdly strong AOE, and having 2 reliable lockdowns both with 15+ turn cooldowns does not mesh together, especially when one of them can't be prevented by one of those lockdowns. You can survive one rotation, but surviving another is absurd, much less dealing enough damage to actually defeat her at the same time with how much HP she drains back from attacks. Kuuem No1 being a fight that you didn't want to drag out was supported by the story, given her insane regeneration ability, but for Idea, there's nothing to the fight beyond raw stats. I'm guessing there was the intention of making the unvieling gimmick be the solution, as it seems to prevent her from using her normal skill and instead do the SP drain, but again, that's inconsistent at best. Sometimes she doesn't do the move until the turn later, and occasionally she'll randomly target someone who didn't even do the unveiling move in the first place. I can't exactly plan a strategy around something that only sometimes works in the way it is meant to.
None of the other games had this degree of stat-gatekeeping battles, as while Reincarnations were there as an option to brute force things with raw stats, the majority of your power came from resetting and re-mixing your skill trees to better suit the fight. Here, that isn't an option for the reasons I mentioned. You can't bring a magic team, because Kuu needs to stay on healing, and Faria doesn't deal enough raw damage by herself to deal with the fight. You need gear to block those ailments, so you can't use equipment to support your team as much, and the sheer amount of health and damage the boss has means that if you don't hyper level, you'll spend too much time trying to heal up that you can't actually inflict enough damage.
This is a reoccuring issue I've seen with Kludge compared to the other games. Just naturally going from one event to the next, for most of the series it's all been perfectly fine level-wise. It was only when you reached the super bosses of the extreme late game that you
needed to start grinding for levels to even fight them. Going from the Ancestor of the New World to the bosses of Raktass in Blight, going from Siblumi to the Descendants in Awake, and going from Shin to Trau in Colony, it felt very smooth and even if grinding would have made some fights easier, it wasn't ever required. Here, going from Dita/Core Remains to Kuuem felt like I was barely able to eek out victory by swapping stuff around and restrategizing, but going from Kuuem to the Mechagods felt like a sheer cliff, and going from the World Border to Idea feels like I need a rocket ship to even attempt with how suddenly and drastically the stats spike up.