The line you've drawn between these effects is false. Burnout and Domain Amplification are not in any way comparable to Technique Extinguishment, let alone the higher output of Jacob's Ladder. Burnout doesn't even neutralize your cursed technique, it just becomes ridiculously difficult to use. And Domain Amplification "neutralizes" cursed techniques by allowing the opposing cursed technique to flow into the """space""" where the sure-hit technique would normally be.
This is not at all similar to the three anti-curse curses in JJK (BR, ISoH, JL).
I never said anything about DA allowing an opponent's technique to flow into its space. I'm talking about DA preventing the user from using their own CT, which has nothing to do with what you're saying.
Besides, it was never shown, implied, or assumed anywhere in the series that JL can outright end Kenny. The only point you might be right about is CT burnout.
My previous argument about these not being the same as technique nullification applies here. And beyond that, Technique Extinguishment nullifies all jujutsu, the likes of barrier techniques included.
She can only nullify what is within her scope, not something beyond it. She only nullifies barriers that she can directly access; she wasn't nullifying the entire Culling Game.
All she did was create holes in the barriers and move around the other colonies through those openings.
The only reason Jacob's Ladder harms Incarnations is because its effect breaks down the cursed object inside them, and Sukuna was gonna die if not for his Oscar skills and Yuta turning off the technique to save Megumi respectively. Also, all jujutsu ultimately stems from the brain, so obviously Technique Extinguishment is working on it. I hope the irony of you so confidently accusing me of not reading isn't lost on you.
It normally has burning effects. It isn't nullifying cursed objects when they're merged with other people.
Besides, Kenny isn't even a reincarnated sorcerer. He has an active CT that allows him to replace and control Geto's body. JL works in a similar way to DA: when DA is active, users can't use their CTs, and when JL is active, opponents can't use their CTs either.
Once they escape the light, they can immediately resume using their techniques. It isn't nullifying the brain itself. The light only nullifies what it can directly touch.
So, at best, it temporarily prevents the external use of a CT rather than permanently nullifying its source.
It does matter, because the looming "We gotta jump Sukuna" is a MASSIVE deal that influences every decision. And speed does not really matter for a sneak attack, you won't react to something you can't sense coming. SSK is only needed for a fight, not a sneak.
Speed does matter, and besides, non-CE weapons aren't doing anything to Kenny. She isn't physically one-shotting him either.
She definitely needs the SSK to kill any heavy-hitter-level opponent.
Are three incredibly-short paragraphs so awe-inspiring you think I'd need a chatbot to manage it?
Yes
Hana was not to participate in combat due to being disabled and incapable of cursed energy reinforcement, she was only to act a final card to be played in a worst-case scenario if even the Yu-jo plan failed, to try and save Megumi (Hana's love)/destroy Sukuna (Angel's nemesis).
You say JL can instantly kills Kenny, but if that were the case, CE reinforcement wouldn't matter since Kenny would be cooked instantly.
She also has a ranged attack with JL, so the cursed spirits wouldn't have escaped either. Again, that doesn't require CE reinforcement on herself.
Yuta was needed to deal with Sukuna, yet they still sent him to sneak up on Kenny rather than relying on your hypothetical scenario of JL working on Kenny, which was never implied or assumed anywhere in the series.
As for Hana being the final card, that means nothing. She entered the fight at the end and had enough time, unlike Yuta, who was needed from the beginning to fight Sukuna.
Now you're just making up reasons for why Hana wasn't sent to kill Kenny. It's simple: her technique wasn't enough. That's all there is to it. There's no deeper motive here; you're just making things up.