Why is Hermione upset when she misses Charms?

A couple of months ago, I wrote in this space about the trap that is time travel. It seems at first like a pretty fun and clever device: create a way for your characters to travel back and forth in time and then watch the fun ensue.

But, if you look at the concept too closely, if you explore the possible consequences of time travel on your narrative, you really might want to think twice before you employ it.

As much as I love The Prisoner of Azkaban -- it is, in fact, my favourite of both the books and the films -- I still believe that the introduction of the possibility of time travel to the Harry Potter universe  in this third novel is an strategic and dramatic error on the part of author.

The following passage from about two-thirds through the book jumped out at me recently as I listened to the Jim Dale audiobook version of The Prisoner:

Hermione was sitting at a table, fast asleep, her head resting on an open Arithmancy book. They [Ron and Harry] went to sit down on either side of her. Harry prodded her awake. 

'Wh-what?' said Hermione, waking with a start, and staring wildly around. 'Is it time to go? W-which lesson have we got now?' 

'Divination, but it's not for another twenty minutes,' said Harry. 'Hermione, why didn't you come to Charms?' 

'What? Oh no!' Hermione squeaked. 'I forgot to go to Charms!'

Hermione laments this mistake for some time, to the point where she brings it up later, having found out that Cheering Charms might just be on the exam.

"So what?" you ask. "It's a fun scene. It's neat to see Hermione not quite in control for once!"

And yes, it is an interestingly little scene, intended both to show Hermione in a more vulnerable situation and to pique our interest: just what is up with our favourite witch?

But think about it a little more deeply. We learn later that Hermione is in possession of a time turner, which permits her to travel back in time to attend several classes that are scheduled at the same time. She has been using it all year. As we learn at the start of term, she uses it on one day each week so that she can attend Divination at 9 a.m., then go back in time to attend Muggle Studies at 9 a.m., then travel back in time again to attend Arithmancy, again at 9 a.m.

Once she learns she has missed Charms class in this scene, why doesn't she just excuse herself, travel back in time and attend the class? Rather than freaking out and feeling unprepared for the exam, why not use the time turner, as she has done all year, to travel back and go to Charms?

And then you have to ask yourself: why is Hermione so tired? With the time turner, she could easily travel back in time once she's finished her homework each evening in order to go to bed at an appropriate hour so that she is well rested for the next day.

Say she studies until 3 a.m.. Fine. At 3 a.m., she spins the time turner six times, goes back to 9 p.m., and goes to bed. A good night's sleep follows and all is well!

Of course, if Hermione were to go just that, if she were to re-live an average of eight hours every day in order to keep up with her classes, her homework and her sleep, she would end up significantly older (about four months older) than the others at the end of the school year. Would that make a difference in their lives? Would the others notice?

I'm not sure but, because of the introduction of time travel, these are questions that have to be asked.

And they are just minor questions, raised by the brief scene reproduced above. As I've mentioned before, why doesn't Hermione go back in time far enough to stop Voldemort in the first place? Or at least to the point where Peter Pettigrew/Scabbers is easy to catch?