They were actually pretty inconsistent when it comes to cogged wheels on TM2. Some rolling stock has cogged wheels, some doesn't. The tender wheels are not cogged, not even the new AEG James & Gordon will have cogged wheels on their tenders. At the same time, the small engines sold with 1 truck have cogged wheels on their trucks.
Once I was wondering why they put these toothed wheels on rolling stock, and not just on driving wheels of the engines, but now I realized that these wheels are really useful on the somewhat problematic track elements like the steep curved slope (some lighter wagons without cogged wheels tend to derail while descending such slopes), especially when that curved slope is followed by another curved slope, and you need two slopes - curved or straight - to reach the appropriate height for the bridge under which you can place an operational track:
It's better that the curved slope is not immediately followed by another one, so I placed a normal curved track between them. Note that the barrel delivering specialized truck from TM2 "Cassia Crane & Cargo Set" for some reason also doesn't have cogged wheels, and that makes it unstable on some elements (curved slopes, "Head-to-Head-Crossing", etc.)
So yes, it's strange that Carly's wagon doesn't have cogged wheels, and we still don't know what the wagon is for. I don't think that she suppose to pull just that wagon; it looks like something should be placed on it. If that something is push along Sandy, then that wagon will be pretty heavy, and could derail on a steep curved slope without the cogged wheels... I thought they would make all the AEG rolling stock with cogged wheels. They are ugly, but you can hardly see them when the vehicle is placed on the tracks. They greatly contribute to the general stability of the vehicle, and prevent derailments on problematic track elements.