Night of Joy is primarily attended by teenagers who are sparsely supervised. Imagine the park operating with only the Brazillian tour groups in it. It is by far the worst time to be working at the parks followed by New Year's Eve after they give out all the noise makers.
For example Grad Nights, at least in my experience, was pleasant as they used a TSA-style entrance complete with clear bags for belongings only and a pat down. This was coupled with School specific punishment for trouble. With Night of Joy, you have no repercussions (short of divine intervention) and the ratio of child to adult is a lot larger.
They also close many attractions not as a cost savings measure, but for safety reasons. In preparation for the event they also sweep the park for any freestanding objects that are not bolted down. In fact, the park has to increase the number of security working as well as have additional OCPD on hand.
By moving the concerts to the Sports Complex, Disney doesn't have as much bad press as if they cancelled it outright and it allows them to add more time to the shows. Disney will also win because now the NOJ ticket holders will presumably be at the park with normal Guests. This will cut down significantly on the obnoxious behavior and group mentality.