(Chris's PoV)
Leaving the academy is simple.
Students can just leave on their own or take a mission before going out. There are no restrictions, except that everyone has to sign when they leave the academy and once again when they return.
Though it appears to be a hassle, the academy implements this so that they can know who are still in the academy and who aren't. This is to know if a student disappeared, they would know if they disappeared while outside or when inside the academy.
Though the inside of the academy is supposed to be safe, no place in the world is 100% safe. In comparison to other places, the academies are safer but also the most dangerous places to live.
Every evil one out there knows the best way to obstruct humanity's progression. It's to destroy the young generation, who are the future of humanity.