Death in the academy would be investigated, and with the assistance of the badge, it was easier to investigate.
But things are different outside the academy. They were all on a mission to eliminate at least 5 titans to complete the basis of the mission. For the average first year student, this mission wasn't particularly easy, but it wasn't so difficult either. As long as they weren't surrounded by a group of titan, then it was easier to deal with them one by one.
However, this city as been overrun by titan and even gigantic beast, if one wasn't particular careful, one could lose their life without having any idea how they even died.