Child doesn't want the door closed - Silent Return

First of all, what do you want? As the parent, you should be able to decide if you want your child's door opened or closed. Some houses are just not set up for bedroom doors to be open because the child can see light, sounds and people walking around. Some parents don't mind if the child's room is set off from the living area. So, first off, decide what you prefer. 

From a fire safety standpoint, it is safer to sleep with the door closed. In case that factors into your decision or gives you something to share with your child. 

If you are okay with it being opened a crack, then you can use that as a big reward for your child following the sleep rules. If they are struggling with the limits and continue to have the door secured but are verbalizing wanting the door open then you can offer that as the ultimate immediate reward. "if you stay in your bed and don't come out, I'm happy to leave the door cracked. But if you come out, it has to be closed." 

If you do this, only offer this option one time at the beginning of the night. If they loose it, don't let them beg for another chance. They can try again the next night.

I would avoid offering this option with your child if you think it will turn into a game. I would also avoid offering this option if your child is no where near being compliant. You don't want them using this as a manipulation tactic. If you see them trying to use this as a game just remove the option totally and say you can try again in 5 days once they have shown that they can follow the rules.