Yes, people misunderstand torque, power and energy .... and I would like to add speed. Sure it takes energy to spin a tire but that doesn't mean it's applying that energy (or torque) to the ground. For that reason I say for this discussion it is best to imagine the weight of the wheel can be disregarded. Imagine it doesn't weigh anything.
I disagree with your sentence I underlined.
Lets say we've got an open differential and one tire is on glaze ice. You can't apply much torque to this tire before it starts to spin. Lets say only five foot pounds of torque can be applied before it spins on the ice. The other tire that is on dry pavement is also getting exactly the same amount of torque (5 foot pounds) but this is still not enough to move the jeep.
This is why I say an open differential ALWAYS applies the same amount of torque to both wheels.
On the other hand a locking differential will, at times, apply all the torque to the one tire with the best traction.
For example lets say a tire on a jeep comes off the ground due to very rough terrain. (Imagine he's in 2 wheel drive, I don't want to think about what the other axle is doing). In this case the tire on the ground is getting all the torque and can still propel the jeep.
I say no torque can EVER be applied to ANY tire that is off the ground. This is true if you have an open differential or a locker.
All my off-road buddies disagree with that last statement. If the jeep has an open differential the tire off the ground would be spinning fast. My friends would say the spinning tire would have lots of torque. "Go grab that tire, Dave. You'd go flying up into the tree tops."
1. A spinning tire of any weight will be hard to stop. This is why I prefer to say it has neglectable weight for the sake of discussion.
2. If the spinning tire isn't pressing against the ground it CAN'T be applying any torque. To disagree would be to disagree with Newton's 3rd law, to every action there must be an equal and opposite reaction.
To explain my last point it would be like me going into a gym and bench pressing an empty bar bell. If I were to yell out "I am pressing up with 300 pounds of force." Everyone would yell "BS!" It's not possible.
Then lets say a couple of guys were to put 300 pounds of weight on the ends of my bar bell while I am holding it above me. Now I sure as hell better be able to hold up 300 pounds or that bar bell will come crashing down on my chest.
On the other hand lets say I can bench press 300 pounds (a lie) and when that much weight is put on my bar bell I continue to do repetitions. Now everyone would say "WOW he can press up that hard. I guess he was always pressing up with 300 pounds of force like he said." NO NO NO just because I CAN bench press 300 pounds doesn't mean I was when there were no weights on my bar bell.
This is all hypothetical, I'm a wimp and can't bench press 300 pounds.