When you look at the vast number of Christmas games that are actual Christmas games, you'll notice that a lot of them are not very good. A great deal of this has to do with the fact that Santa Claus, elves, Mrs. Claus, presents Christmas and whathaveyou are not exactly what one would call money spinners when it comes to video games. Can we do better with this? Yes, we can. Should we, though? There's the real question.
The vast majority of Christmas games are offsprings of something else. A big example of this are the movie tie-in games such as The Grinch on Dreamcast and Home Alone on a lot of the earlier systems. This brings a lot of stigma to the notion of Christmas games, because movie tie-in games are nothing that you really want to be associated with, aside from rare exceptions.
The popular point is to attach movies that feature Christmas, hence why Die Hard was brought into the mix years before. Honestly, bringing good movies and some actual good movie tie-in games to the fold gave me a legit reason to put "(usually)" in the title. Die Hard Trilogy and Die Hard Arcade (which has nothing to do with Die Hard, aside from the title) can be called actual Christmas games, but not at all themed Christmas games.
Spider-man Miles Morales is a popular example of gaming now with Christmas elements in it because it took place during the season. While the game is good, it is still short and wholly unsatisfying. Still, the sequences with the family at Christmas was quite nice and heartwarming. If this sort of thing can catch on a little more, it can definitely be something that people enjoy as an aside to the main game elements.
Then we have games like the Elf Bowling titles that go full tilt into the theme of Christmas. Anything else that comes out of this "franchise" is terrible, but at least the games were mind numbingly fun enough. I've never played Rudolph the Red-Nose Reindeer for the Wii myself, but there are times when we can just let assumptions play their part. I no longer have a Wii and I most certainly am not paying $20. Yes, I know there's a DS version and yes, I do have a DS, but the answer is still no!
Now, is there a way to make full, rich, awesome Christmas games? Of course! A game that has Santa deliver toys in a free-roam game with dangers, time elements and mechanics sounds like it definitely could work. There are plenty of games ideas like this that can be as G or PG rated as they want, but that would be a great big challenge for them and publishers today aren't with that sort of thing. Trying new things? That never works. Let's just make another Call of Duty Modern Advanced Battle Trash Edition. Shove that in your stocking! With love!