I think this depends a bit on how exactly jinsung is being hampered by the state of his arms. it doesn't look like he has trouble using any technique. Nor motivation to risk big techniques... He shouldn't have trouble using the dragon tiger gate as the technique does not require any physical strength at all. He even used it successfully against kallavan while his arms were almost paste. I do think landing a floral butterfly type technique is probably specially risky against anima. Since you can get hit by their anima while landing the technique even if you successfully use reverse flow control on them beforehand...
The LPB definitely lose their edge if they lose their anima, no discussion there. Though the same could be said if the arie lose their arie swordsmanship or the ha their reinforcement.. I feel like you aren't giving the LPB any credit for their non anima skills though. Pudily has still taken head on the full blunt of jinsung's CQC and even actively looked to engage him that way. Elaine is absurdly good at using her reel. the LPB princess was able to take on hatz swordsmanship. The other one was a match to androsi in physical combat at least. And neither showed their anima at all (and left with the implication that their anima were heavy hitters). Considering elaine's background.. their anima must be pretty special just in general. The LPB family has anima and aptitude for a wide variety of combat forms... even if they of course lag behind families who specialize in said combat forms. I disagree with the idea that the LPB are the weakest family... I maintain they should be at least better than the families whose attributes aren't ideal for combat or less than meta (which would include the po bidao, eurasia, tu pirie and hendo lok families). In my head the situation is more or less like this:
top 3: Arie, khun, ha.
Prime meta attributes, strong bodies.
Middle of the ground: Ari, LPB, yeon,
At least excellent combat attributes in general but not as special those above. The ari are weapon users but strictly inferior to the arie. The LPB stand out due to their anima. Anima are BS. Hana is both a fisherman and a wave controller... Which is as meta as it gets.
Weakest: po bidao, eurasia, hendo lok, tu perie.
Generally not combat or prime combat attributes, excel at support. I am a bit on the fence about the eurasia since blosom's thing seems to be offensive wave controlling, based on that she might deserve a spot above.
do note that is meant to be extremely general. Individual cases of members of the families standing out are a different thing. Yihwa could end up being stronger than ran, the strongest non irregular we know comes from gustang and blossom (boosted by zahard's blood).
I rank the FHs/families almost equal as you. In a 1v1 against each other, context and dynamics of battle is important
FHs:
On the top, Hon, Eduan, Yurin, probably in this order. Don't need to explain why.
On the bottom, Tperie, Bloodmadder, Gustang, probably in this order as well (ascending, from weakest to strongest).
LBs simply aren't suited for 1v1, and Tperie must be that wise all knowing dude that isn't as strong as his peers.
Bloodmadder sucks at 1v1 because he probably has no offense, if he had, he'd be comparable to Yurin. If you don't have enough offensive to beat your peers, then you're just a persistent punchbag. And if you do have offensive to beat your peers, then the fact that you also have stupid durability makes you a monster, his niche would overlap a lot with Yurin. Also, Bloodmadder decompressed is ~8m tall, at his strongest/highest durability he's a big target.
Gustang because he, too, fulfill the trope of the intelligent, knowledgeable, "scientist" that lacks in power so he knows how to conquer the world but does not possess the means to do so (strength), that's why that individual is executing a big plan and all that to gain the strength necessary to conquer the world or do so by other means. Just to clarify, I think Tperie's shtick is more towards being able to know anything (his lighthouse is an unique names "Eyes of God") and all that but who doesn't give a f*ck about any field of knowledge while Gustang is the ultra nerd that systematically studies everything that exists in this world. Also, Gustang is specifically said to be weaker, less talented than Blossom, her being an offensive WC and him more of a supportive type.
That leaves Hana, Blossom, Traumerei, Han in the middle, in this order (descending), I think.
Hana is said to once have surpassed Yurin when angered. She also has both fire powers extremely destructive (they should be much stronger than Evankhell's) and healing powers as well. Her powers (high offensive and healing) matches well against large targets (Shinheuh), high defense (Bloodmadder, Yurin) and since her theme is fire I expect her fire to be stronger than whatever Shinsu techniques Blossom or Gustang use.
Blossom should be solidly above Gustang and she + him birthed one of the two strongest princesses, while Gustang has every narrative reason to be one of the weakest FH. Her abilities should match well against Shinheuh as well, WCs can fight at distance and with large scale and AoE attacks. And I expect Han to suck, so it's her or Traumerei.
Traumerei because he should win against Tperie, Bloodmadder and Gustang. He's a control freak and ingenious, he wouldn't go to war against Gustang if he specifically can't handle him, since that'd put his Family/Army at more pressure having to compensate for his shortcomings. And I expect Han to suck, so he's above Han. I also expect his Shinheuhs/Anima abilities to not match well against Irregulars in general because they have broken abilities and talents.
I expect Han to suck because I think he's going to be be the weaker, less combat/strength freak of the Hon, Han pair (they're probably relatives). Hon is probably power hungry and values strength, Han and his family are pacifists. Hon is the strongest FH and has Arie swordsmanship, Han should not have anything of the same caliber.
About the families, what changes is that the Hendo Lok family is probably the weakest for obvious reasons, maybe the Eurasias should be higher than Yeons, the rest should remain the same.
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