There's a lot of good reasoning in the existing 4 other answers, but they all miss something, even if they graze it.
Yes, these ATV's are highly valued as motors, but that makes them great for bait in an ambush.
At first, I can see many of these machines being used for combat and anything else that can be done with them, foolish or not. I mean, just look at how people use them now.
But as they become more rare and as people realize just how many things they can do, and then come up with really valuable ways to use them, they will be used less and less for combat, for the most part. There will still be some Generals that are so vain they "require" the use of the Royal ATV as their steed, or whatever. And there will be people and countries that will go looking to acquire/steal them at any cost, even if it's to hoard them and prevent anyone else from having them.
So some of the best armies will have these machines, regardless the risk. And the smart armies will use them to bait enemy into traps. The best way to catch a thief is to catch them in the act and the best way to do that is to make it a controlled environment for the captors. This works on a group as well as an individual.
A larger army may not be as easy to get into a trap as a burglar, but that's why you use the size and difficulty of a trap and bait to match the quarry. One ATV might not catch the eye of a General, but it could a Corporal. Five ATVs might engage a Major. More than that, plus you make it hard on the army to catch the ATVs so they stop looking for traps after the first couple miles/kilometers, and you might just bag a Company and some higher ranking officers. Even if those officers aren't in the trap, they could now be fairly insufficiently guarded so they could be rounded up later or a secondary group of soldiers could capture them while the chase is still in progress.
Could they still be used on combat? Sure, but that's a high risk and low reward situation that can be altered by simply using more people so it becomes less risk (the to Crown) and higher reward in that you are overrunning the enemy by just pure mass of people, which was the tactic of many armies even after guns were introduced. (Look at WWI, for instance.)
There may be limited use with specialty troops that harass any army into engaging before they are ready, or that quickly flank rearward artillery or other long range weapons, but that would be a relatively small group and the reward would have to be extremely high to merit the high risk of losing these valuable machines. Likely, these troops would be using the ATVs that normally tow the larger war machines, like cannon and Gatling guns.
Could they be used in the supply chain? Sure, but the supply chain itself is a high order target for an army. It has fewer soldiers and can serve to supply an enemy army. Adding high value ATV's as the motive power for these supplies will increase your need to have a large force guarding it to the point where your army might as well just surround the supply chain. Unfortunately, this doesn't really get you very far when your army has to continually to return to base to guard the next shipment of supplies to itself.