[quote=@Bishop]
Wait, so we can have powers although we are simple students just awoken from the [s]Infinite Tsukuyomi[/s] brainwashing?
[/quote]

Excellent Question:

Imagine the essence of desire, of free will and want, not as a concept but as a thing, a type of energy signature or radiation that is part of the chemical make up of the soul. The same goes for its equal and opposite, Purity, the energy of the angels. Whenever one of the energies spike, it goes beyond the ethereal and materializes into the physical as power of some kind. Desire in particular shaping the power to fit the desires they have. Whereas Purity enhances a person based on their resolve to live by your standard virtues and what have you.

"But wait, The Purity energy completely enveloped all of the soul of everyone, didn't it? Wouldn't that count as some large spike of energy and give everyone angelic power?"

Not necessarily...

To begin with, that desire energy was considered a taint, a stain of corruption within the mortal soul. The soul was never designed with desire in mind, it simply "infected" everything formed from Purity like a plague. The brainwashing in question is a result of desire as an energy being completely erased by the purity, which fills in the proverbial empty space it leaves behind. essentially akin to returning the soul to "factory settings" one could say. A surge is the result of that energy being so potent that it breaks out of the soul and becomes actual energy, whereas the Angels simply filled in an empty space of the soul, keeping the energy contained within. There's a reason for this, but I'd rather not discuss it here, for the sake of Spoilers.

The moment your characters touched the corpse, the energy of desire came flooding into their soul in such a quality and quantity, that it generates a soul surge.

TL;DR: Overabundance of literal will power result in it pouring out of the soul, and into the physical world, becoming actual power for the characters in question to use.