The extra meetings, parent phone calls, planning, stressors, fires, etc that are on the shoulder of the HD.
Many band directors choose to stay the assistant because it’s too much to deal with at the HD level.
And most all kids are good. If you have ‘bad kids’ in your program and you’re referring to behavior, it’s a culture problem created by the adults. If they’re ‘bad kids’ because they need more time and patience on their instrument, then give that to them.
All in all an assistant may teach more kids and classes (depending on the program), but the pressure and stress always ends on the shoulder of the HD.
Don’t go into this profession with a chip on your shoulder like that. You will get squashed immediately. Be a team player.