The thing is that soulhax wouldnt work since HR is actually fully capable of dispersing such attacks and its not solely only because of fiamma having soul resistance.
"A restraining spell created a thirteen-sided object around Fiamma, not only restraining Fiamma's actions physically but also separating his flesh from his soul. He was trapped in a "woundless bind"; nothing more than a hollow existence. [...] "Fiamma could hear nothing, but the Pope's mouth was still moving. "From this moment forth, you shall be bound for forty years. Sample the 'loneliness created by oneself' that Judas experienced, and correct that immature soul of yours." [...] Inside the thirteen-sided object, standing in stupor, Fiamma's lips give a slight twitch. The sign of final resistance he was making with all his strength. [...] "Give up. I am the Pope of the Roman Catholic Church. The power I wield now is the Holy power of two billion followers passed down through two thousand years of history. It is not something that can be destroyed by just one person." In addition to this, the Basilica di San Pietro was the largest and highest stronghold of the old power. Combined with the power of the Vatican, these things could be said to be powerful spiritual items that could increase the Pope's strength. [...] At that moment Fiamma's voice was heard, "Hmph." The Pope expression twisted into one of shock. This was not something someone who had been bound by such a spell should be capable of. Fiamma's voice adopted a light tone, "How pitiful... just two billion followers? Only two thousand years of history?" The world disappeared. [...] The Pope barely managed to see the thing which appeared on Fiamma's right shoulder, alongside a bright light from his eyes, because the very next moment his vision was engulfed by empty whiteness and a violent storm destroyed his surroundings. [...] There was a strange thing above his right shoulder. Different from the two arms he possessed as a human, like a wing that hadn't developed properly, it was a huge, malformed hand with four fingers on it, composed of blocks of distorted light. It was told in Greek legend Athena had hacked her way out of the forehead of the King of the Gods, Zeus, and climbed out of the wound. The scene in front of the Pope was similar to that legend: Both were entirely unbelievable."
(Toaru Majutsu no Index Volume 16, pg 193-195)
The Holy Right's defense self activates and disperses Pope Matthai Reeses spell 'Symbols of the Son of God and the Twelve Apostles' backed by 2,000,000,000 followers and the spiritual items of The Vatican meant to bind the physical body and remove the soul
He dosent need to lose his soul to lolnope the mindhax since HR can swat things of that variety away no diff
