I think you will find that parents expect to pay you LESS because, well, their kid is "just sleeping" wherein it is actually a specialized care option and that should cost more, not less.

There is no way in hell I would do this. Nope. Too much potential for hassle and what about liability? What happens when you are asleep and some dckid gets up and hurts themselves or worse? Sure, it can happen at home too but since you are paid to care for the kid you know the societal double-standard would rear its ugly head. Suddenly you are found responsible because some 4 year isn't even parented enough to stay in his bed. Now the failure of his parents are YOUR problem.