Note: in the interest of readability I'll number these, and numbers in the counter-argument section will be related to the same numbered piece of evidence here.
1. Jiraiya's explanation of how genjutsu works.
Step one - target your opponent's senses to gain access to their chakra network
Step two - manipulate the chakra flowing through their brain, producing the effects of genjutsu
2. Genjutsu is countered by disrupting the flow of chakra.
If the target has stronger control over their chakra than the genjutsu user they can break out of it solo. If the target doesn't have strong enough chakra control then they won't be able to break it and need a third party to inject them with chakra. The only logical conclusion to draw from this is that the chakra being controlled is what allows genjutsu to have any effect.
3. Genjutsu never worked on anyone without chakra since everyone in Narutoverse has chakra.
As Naruto explained to Kawaki, not using chakra =/= not having chakra
When Kakashi taught Sasuke Chidori he said that if you overdo it and completely run out of chakra you'll die. He later proved this to be true against Pain
1."Jiraiya didn't say word for word that genjutsu works by controlling chakra."
No, he didn't say exactly that verbatim but you can't simply stop reading after this part of his explanation
Jiraiya made it very clear that chakra in the brain is key. Of course senses are also very important... Most visual genjutsu wouldn't work on a blind person, for example. Sight is the vehicle through which a visual genjutsu user gains control of their target's chakra.
2. "People have broken out of genjutsu with pain instead of chakra flow disruption."
We've established that senses are linked to the chakra network right? It stands to reason that a burst of pain would also disrupt chakra flow and that's what is breaking the genjutsu. Not the pain itself.
3. "Hagoromo is the one who gave people chakra. Kaguya's Infinite Tsukuyomi worked on everyone before that."
Infinite Tsukuyomi is the sole exception and goes against two major rules of genjutsu already:
- Can't be broken by a third party disrupting chakra flow. This is extremely important and suggests that IT is fundamentally different than all other genjutsu.
- It's a visual genjutsu that doesn't even require a line of sight to the target.
So, sure, Infinite Tsukuyomi works on people without chakra but it in no way represents how far inferior abilities work or what they are capable of. Arguing otherwise is like saying a match can burn through a fireproof safe because lava melted one.
Genjutsu does indeed rely on the target having chakra to manipulate. Should you want genjutsu to be a factor in a cross-verse battle then all you'd need to do is equalize whatever energy the other character uses to chakra. Easy. And let's be honest... if "genjutsu gg" was the only conceivable argument in a thread where energy isn't equalized then that battle is probably a bit of a mismatch anyway. Naruto is my favorite series and it's ok to admit that a character from our favorite series would lose in a hypothetical fight. It means less than nothing :)