I suspect we are saying the same thing, or at least reaching the same conclusions.
Where we differ is this:
The grounded wheel doesn't turn not because it has insufficient torque as you state but rather the power is diverted to the least resistive path to the flying wheel. In fact the applied torque may be perfectly sufficient to move the object.
We are not lacking torque per se, rather we are simply lacking resistance (traction), and thus the power to the right wheel.
Because torque is the result of the engine power working against the available traction, there
is zero torque on the flying wheel, and therefore zero torque on the other wheel, due to the open diff. (OK, not quite
zero, because there is the friction of the wheel-bearings, air resistance etc). How much torque the engine
is capable of producing is irrelevant - it's unable to use its potential to generate actual torque.
As I said in a previous post, if you imagine a sensor on each half-shaft, showing a continuous readout of the torque, it would become clear that neither shaft is under torque.
So the reason the grounded wheel fails to turn is simply that there isn't any torque available. Although there is traction at that wheel, the engine meets no resistance from
either side because the more the pinion tries to turn the ring gear, the more the diff just speeds up the the flying wheel. No resistance, no torque; no torque, no power!
The reason it gets complicated to talk about power, is that a diff doesn't share power between both sides evenly. If the torque really is zero, then so is power, and it's pretty simple. But as soon as the spinning wheel is no longer flying, but in mud, say, then we have some (equal) amount of torque on each shaft. But because they are turning at different speeds, they have very different amounts of power (power=torque x RPM). (If one is actually stationary, it will be is generating no power, even though it is generating torque and force!)