I know a lot of teachers and they all leave tests (not examination papers) on shelves in their classrooms/labs. It is very rare (almost unheard of) for a pupil to look or take things from teachers’ shelves. This is because of clearly stated and known meaningful consequences (detentions, parents being called etc)
Strangely enough, I know a lot of teachers too, in both Ireland and the US, and if any of them left tests on a shelf they would face disciplinary action.
The reason is that the consequences for the children of cheating on the test and being found out are so great that it is considered completely unfair to leave temptation in their path. Cheating goes in the student's permanent record. They will earn an F in their course for a single incident of cheating or plagiarism that is discovered.
Same principle goes for Christmas presents - if Christmas is a big deal, if you and the children have been looking forward to it all year, if it means so much to you to see DCs all surprised and happy on Christmas morning, hide the presents well. If Christmas is so big a deal to you that ruining the surprise ruins Christmas, then don't leave it to chance, and don't put all of your expectations for a successful Christmas in the hands of a child.
You can use appropriate consequences as necessary all year round for children who eat the dessert for that night's dinner at 11am, etc. This is a safely low stakes event and the response of the parent will probably not be coloured by any major emotional investment, unlike the Christmas scenario. Children can learn gradually what their own priorities are and how they can compromise in order to fit in with the expectations of others. The only thing a smart child will learn from draconian punishment at Christmas is how to re-tape presents properly.
(As an aside, if you have a lot invested in the Christmas morning experience, so much that you are left fucking furious (or words to that effect) that a child did something completely predictable and normal with presents left out, then you need to sit down and try to get to the bottom of your expectations of Christmas, and ask if it is appropriate to expect the child to create your Christmas experience, or whether Christmas offers something for the child too.)
In this case, the child spends time with both parents in separate houses, and the child has been a bit of a handful for a little while - I think a parent needs to poke around a little and figure out if there is something in that situation, juxtaposed with all the 'family' themed hoopla around Christmas, that is making the child upset. Christmas is a hard time for children if they have two sets of parents to do Christmas with. It can develop into a case of performing Christmas for the parents, twice. This can be the cause of unhappiness in children as they take second place at a series of faux events that is just the one special, child-centered thing in other people's families.
(As another aside, it's probably not a good idea to place desserts, chocolate, etc on a pedestal by dishing out punishment for eating these items and not, for instance, for helping themselves to cheese. You only reinforce in a child's mind that there is a hierarchy of food with sweet things on top if you do this.
I would not punish a child who ate only his own portion of dessert/chocolate, etc. He only hurt himself after all in so doing, and I would have given it to him later anyway. Children can be allowed a certain amount of choice in the timing of their meals, desserts, snacks imo, with natural consequences to choose from. If a child feels miserable that everyone else is eating dessert after dinner but he has already had his, then he can be asked to ponder his priorities.
If he ate everyone else's too, however, then that would merit a punishment - not because sweets are special but because he took away everyone else's food and obv their choice as to when they would eat it. However, I would suspect a child who did a thing like that would be experiencing some sort of massive brain fart or some issue that needed addressing by means other than the handy/lazy one of punishment alone.)