An idea:
Have keyrings for specific positions (sound operator, lighting operator, spot operator,
etc.) that are passed out at the beginning of the day by an adult and collected before you leave the building. They should open only what you need to access without immediate supervision (booth doors, amp/effects rack, stairs/ladder to
catwalk or door to lighting cage.)
You could just have an adult open the doors for you, but if you need to go to the bathroom,
etc. then you either leave the door open to everyone else (insecure) or you need an adult to come up the stairs and let you back in (a waste of everyone's time).
But keys to equipment storage (like for microphones, cabling, gels, headsets,
etc.) should only be held by the adults. You should not be able to get at that stuff without an adult right there with you. That would be a serious liability.
A keyed
power switch is totally unreasonable. That sounds like a
power struggle thing to me; you want to make sure you can control who uses the equipment. Only an adult should be capable of making those decisions. If they want to let someone else run the sound board they should not have to
track you down to get the key. A locked
power switch doesn't prevent theft; it prevents use.