Why does LEGO avoid 2x4 plates on these occasions?
While it's unlikely that we would get a somewhat official answer on this, there can be a multitude of reasons for that, some logical, some economical, some motivated by marketing. Of course, there are some more obvious reasons for the sake of the build and the art of LEGO, but they might not apply in the case of a calendar:


Design. This isn't necessarily the case for using 2x2s over a 2x4 in a calendar. But for example think of something as the Architecture Robie House, where they used 1x2 and 1x1 plates, about 1000 in sum, to simulate the actual brickwork of the real house when they could as well have built it from much fewer bricks. While this also significantly increased the part count, I would still argue this was primarily done for its aesthetic value and it works.
Reusability. Again not too relevant in the case of a calendar, but a lot more important for something like a Creator 3-in-1, when building something else from the pieces is not only encouraged but intended and part of the product's appeal (you could say it's implicitly part of the appeal of LEGO bricks in general, but that's not necessarily reflected in the actual marketing and business philosophy anymore).


A more economic look at the situation opens a few more possibilities that might apply more specifically to your case. While LEGO certainly has more freedom by basically holding all the cards, I found it sometimes helps to think about your own MOCs and why you'd choose one part over the other. When designing a model the first intuition is to use the most fitting part, but there are various considerations to switch them out, almost all of them economically motivated:


Available colours. This is certainly the strictest consideration since you can't use a part that's just not available. While LEGO would have the freedom to simply create the part in that colour, there are still considerations of bringing yet another unique colour-shape combination into production, especially if you don't need it in too many other sets, above all something as much of an afterthought as a calendar. Though, this might not apply so much to something as simple as a 2x4 plate, there's still a ton of exotic colours that don't even have that, even if white is anything but exotic.
Item price. Now for MOC designers, this is motivated a bit differently, since the price of a piece isn't driven "naturally" by actual material cost rather than "artificially" by the demand and supply created from its availability in official sets. That's why 2 2x2s can be much cheaper than a 2x4. But even for LEGO, who basically could mold as many parts as they want, this isn't really driven by material. The material really costs about zero, no matter if you print 2 2x2s or 1 2x4. It is the factory configuration, the logistics of bringing pieces to together, the use of the piece in other produced sets. These all figure into the production cost.
Lot count. In fact when designing a MOC, especially if I intend to build it myself, another consideration is keeping the lot count down. If you already need 2x2s anyway and you don't need a 2x4 for structural integrity, then it might improve your model's acquirability if you have to shop for 1 lot less, since someone offering 5 2x2s is likely offering 7, too. I'd think this isn't too much different for LEGO if you consider the above points about the logistics of molding parts and then packaging them into a single set. Better mold two more than bringing another machine configuration, production lane or, god beware, factory into the mix. And in fact, I often observed that in official sets, where I wonder why they'd use two parts instead of a more fitting one only to see that there's already 20 more of those two parts in the set and it starts to make sense.


All these factors are driven by purely economical reasons and based on the assumption that production and logistics make much more of the cost of a piece than just its material, especially when amortized over tons of pieces and when the difference in material between 2 2x2s and 1 2x4 isn't that big to begin with. But of course there could be another, still economical but less directly, reason based on marketing:


Part count. As noted in the question, this might very well be to just amp the part count of a set, or a calendar where the individual part count of the models isn't too high anyway and you can basically increase it to quite some degree with just adding a few more pieces. A higher part count makes the set seem more valuable (since it suggests more material and a more complex design). This can be the truth but doesn't have to, depending on what factors you measure value by and how it's practically implemented.


Though, I would agree that structural integrity should prevail over all these reasons since a model that just doesn't stay together is of no use at all. But it can still be relative how fragile is too fragile and you also have to figure into the matter, that the advent calendar is somewhat of a side thought that might not be driven by the highest of quality and design considerations from LEGO, especially regarding the buildable items when many people seem most interested in the figures.