Self propelled steam cars had been in development since the early 1700's. The "horseless carriage movement" had been a thing for a long long time. Steam cars had many technical limitations that would have restricted their military or civilian application beyond novelty.

They were difficult to manage and could not go far without constant water refills. They could only carry a few people at a time. They usually required a road or flat surface to gain any appreciable speed.

Basically, the locomotive was better in every way. It could carry hundreds of men long distances quite quickly and was reliable. In cases where you needed to move smaller numbers rapidly where there were no rails you could take a horse. Investing in such a device would have been a waste of time and money.

As some time has passed let me give you an economists answer; cost, utility, logistics.

A minute of googling says one of these wagons was sold for 500 pounds sterling, the USD to pound rate changed over the war but towards the end was often over $2 paper to the pound. Someone else can provide the cost of a mule powered wagon, but it has to be far less than the $1000 for a steam wagon.

Utility a steam wagon weighs more unloaded and can pull less.

Logistics, you now need a whole host of new parts and craft skills to keep these wagons moving. Also you need to constantly feed the wagons wood or coal which is dense and takes time. Plus you can eat the mules which is not a small matter.

Nothing I can see says a steam wagon is better than mules.