My child doesn't like to have the door closed.

It's up to you whether you'd like to have the door opened or closed. From a fire safety standpoint, having the door closed is recommended. Also, consider the layout of your house. If your child will be able to see or hear people moving around the house, having it open may be too distracting.

But, if your child is adamant and you're okay with it, you can use keeping the door cracked as an incentive for once sleep improves. If they can show you that they can stay in bed without getting up, perhaps you want to let them "earn" having the door cracked. This is up to you and each family's unique situation.