Well, its actually unrealistic for a technologically advanced world to not have any offensive magic using soldiers (or that it would be banned by the world). That would assume that world peace happened, and aggressive invasive alien species don't exist. But considering humans are humans, no matter what world or fiction they are in, not having wars and EVERYONE banning magic is impossible.
The most unbelievable part of the premise is not the magic or transmigration. Its the fact that humans achieved world peace enough to completely ban offensive magic. That, alone, surpasses my threshold of suspension of disbelief.