As some others have mentioned, wildly irregular sleep times can have very bad health impact.
What was not mentioned (from what I've seen) and I now decided to post as an answer instead of comment, so the OP might have a chance of actually seeing it, not the replier I'd have posted that under:
Note, though, that perhaps an irregular sleeping pattern is not the only thing that can be bad. Also enforcing arbitrary, societal wake/sleep times may be bad, as in, forcing something that will ensure someone with not fitting inherently preferred sleep/wake time windows will not perform to their optimum because they are always sleep deprived.
Some scientists seem to reject the notion of "chronotype" - e.g. Satchin Panda in his book The Circadian Code, paperback, p.33 The Myth of Night Owls and Early Birds - he did not cite references for that insistence, IIRC.
Matthew Walker, in his book Why we sleep very explicitly says in the section My rythm is not your rythm that your biologically preferred sleep/wake times were not choice. Basically, the same external synchronization signals (e.g. light) do not necessarily produce the same inner clock phase in every individual. Resulting in some people being able to fall asleep some hours later, or earlier (seems more rare) than others. What was not referenced in the book and I alas was unable to find a reference for quickly, is what I remember about this effect being still present, even though only about half as pronounced, when a group of test subjects was put on an island without artificially stretched length of day / individualized lighting conditions (i.e. electrical light). The "night owls" were still night owls, just by half the amount of hours that they were "in civilization".
Note that this changes over younger age to roughly up to the late 20's or so.
Alas, I do not remember authors names of this.
Both books mentioned, though, will give a lot of insight into all the health down sides of not properly sleeping - for what it's worth.
Some of those may be easily grasped by your young child. I would just plea for really making her understand, as opposed to trying to trick her into obedience with scares - if one does not understand and is convinced of something onself and just uses something as a bludgeon, something will feel off, which I'd say is not good for relationships of mutual trust. (not implying you would, I don't know you - but I guess it could be tempting, if convincing by other means, that might make al lthe sens in the world to the parent, fail)