Should children be allowed to choose their own bedtime?

Yes because then their parents would not choose every thing for their child and the child should choose their bed time because then they know that their parents can trust their child and then they know that their parents are not controlling them

As a mother who have tried that due to child's request I say NO.

Rarely do they understand that they have to pay dearly for staying up (because they will sooner or later) and they will be tired and cranky in school and at home as a result. It also depends on the age of the child. The older the more responsibility, sure, but I also take big part in my children's homework so I know and see to that they don't have to pull all-nighters to pass. So asking about "children" who could decide, their ages range from at least toddler to 18, it will give you different answers.