It appears that you have hit what in Swedish litterature (I fail to find a suitable matching term in English) is referred to as the method ceiling: you have come as far as your current methods will take you, and applying them with greater force will not be effective. You will need to rethink what you're doing, and your title suggests you've already embarked on that path. I hope the question in the title refers to whether punishments should be administered, and not when or how. If not, you'll have a longer way to go.
At this age, your child is dabbling with independence. This is desirable. Soon enough, you'll expect her to make good independent decisions, and that's not a skill she'll acquire without practice. Now you've seen the limited reach of punitive parenting. If you find ways to persist in parenting authoritatively, the next method ceiling you'll hit will be when you are no longer the primary authority figure in her life: if she is not able to act independently by then - a skill you can start teaching now - but still relies on obeying an authority, you will have removed yourself from the equation entirely once she starts obeying authorities you may not approve of.
Yes, she'll try to start arguments. You'll have to excuse her for being nine, her arguments won't be as good as yours, but she has to start somewhere.
You'll note I've used the word "punishment", in place of your "consequence". I hold consequences to be a euphemism for punishments when administered arbitrarily by an authority, but I wouldn't argue with you about terminology if it wasn't for the fact that this distinction also answers your question: staying up late has consequences. And they are actual consequences for the very reason that they're not something you need to arbitrarily decide whether or not to administer. If she stays up too late, she'll be sleepy the next day. She has to learn this. She needs to be able to regulate her sleep, and when failing to do so, she can look to you for guidance. But she can't be reliant on your decision-making here. You don't want to raise an adult who doesn't know how to manage their need for rest.
You can relax. Lean back. Making poor decisions in this domain is self-regulatory.