What I meant to say was, the constant defeats in combat against other demons, combined with Nero's power within Yamato, made Vergil that much stronger when he became Urizen.
Unfortunately, this is where my headcanon ruins everything.
How many of you have played this?
So, according to my theory, Vergil was actually trapped in V, and his Urizen half was just his subconscious acting automatically -- kind of like a very advanced version of sleepwalking. In my opinion, there was no one there, in the same sense you're not there when you're sleepwalking. Urizen is Vergil's advanced autopilot, since he speaks very slowly, claims to have lost some of his memories, and can only remember basic things such as Dante's name.
What does this have to do with Vergil?
Well, Vergil only just now decided to risk splitting himself in half, only because he didn't know which side he consciousness would end up in.
He "lost the coin toss" (where he would have a 50/50 chance to end up in either half) and ended up in his human form.
Whereas, Dante "won the coin toss" and ended up in his demon form.
Where was Dante's human half? Temporarily phased out by the combined power of Devil Sword Sparda and Rebellion.
Devil Sword Dante is his human half rendered subconscious -- which is why Urizen asked how he managed to gain so much power in his final boss battle.
Dante hated and suppressed his demon side, so it ended up taking over. I'm sure Dante would've just wanted to be a normal human with just enough strength to defeat Urizen -- instead, he became more or less deformed due to his own self-loathing.
Vergil suppressed his human side, and therefore, it took complete control and rejected his demonic side completely.
I know it looks like the opposite happened (Urizen rejecting V) but you need to remember how much V ended up regretting his actions both in the manga and in-game. He didn't have his demonic side to assuage his hidden guilt anymore.
Also, being beat up by a conga line of demons is a humbling experience, even for someone like Vergil. He finally was forced to admit that in a weakened state, he wouldn't be able to fight demons, like his brother Dante would have. He depended on the Yamato ever since it devil triggered him when he was young to save him from those demons who found him and his family.
V claims to have had little power left, but it was enough to control three full functioning demons who acted as his imaginary friends due his insanity from his rampant narcissism, loneliness, and constant PTSD from being tortured before being made to submit to Mundus and having his memories erased.
Arkham and Lady also had considerable amounts of power due to Arkham becoming a demon. Arkham's connection to Lady alone was enough to make her more powerful than other humans. In DMC3, her boss profile said she had had "little training" at that point so this supports that theory.
These demons were also on autopilot due to their being magical manifestations of Vergil's nightmares.
So, demonic power can:
- render a defeated demon to become powerful (with the right steps) become human, then have your demon side gain power, then reconnect with said demonic half
- grant a normal human enough power to be a force to be reckoned with, such as Lady through her connection to Arkham
- make other normal humans (who have performed ritual sacrifices) nearly unstoppable Arkham and Sanctus. If you're wondering who Sanctus sacrified, it was himself. It was a risky move, but he most likely made a deal with whoever the demon emperor was at the time in order to be able to resurrect, like Arius did with Argosax.
- allow humans to have just enough power to be a considerable threat (Agnus and Credo).
Now, why isn't Nico powerful? Well, I think she is.
Either her power hasn't fully awakened yet, or they have solely manifested in terms of her IQ.
"Tony Stark built an ark generator in a cave! With a couple of scraps!!"
That's almost the equivalent of Nico's accumulated power. She figured out how to re-calibrate Nero's own sword (in the novel) when Nero himself couldn't figure it out. It's also the reason why she can create such futuristic weapons in the back of a van with nothing but her own resources and a few discarded demon body parts. It's a more advanced version of Nero's demonic power ability absorption.
And if you're thinking:
"But, she's always been this smart." Well, that's because her father, who already had high IQ, had been working with demons (Uroboros and Argosax) her entire life. So this means, just by working with demons, at least some humans are capable of harnessing power in their own way.
Agnus was also transformed when she was still young, so some of that power and/or additional IQ (on top of her already high IQ she has by default) would have just ended up being transferred in any case.
Some humans (such as the Holy Knights of Sparda) were able to fight low-to-mid level demons, but that's only because they've been training their entire lives, surrounded by demonic energy. Being a normal Holy Knight would feel somewhat more like a less powerful version of God Hand and less like Devil May Cry.