Are you implying that a stock full size spare on an OEM spare rim vs a lightly oversized tire is going to make any difference in the drivability of the truck or performance? Because last time i checked 80lbs of groceries in my trunk didnt effect a damn thing just like whats hanging off the rear undercarriage.
Didnt have my coffee... let me try this again. Most cars have donuts not full sized spares. The OEM spare rim is also different than my 20" black so weight difference there also. With TC off im sure limping it home will be of zero issue and do no damage to the drivetrain but I see your point. Then again I am far from a gear head so I am sure someone smarter than me can chime in.
I think there are quite a few spare tire configurations:
1. No spare tire at all.
2. "Skinnier" spare tire - same overall diameter as regular factory tire/wheel but different width (different capacities, speed limits, etc.)
3. Full size spare
Different size left/right tire on rear axle:
I think if you were in 2HI and had a completely open rear differential, there isn't too much to worry about. At most, traction control would engage earlier due to the innate difference in rotational speeds. Other than slightly increased rear brake pad wear, I don't really see an issue.
I'd be interested in seeing how a truck with the eLSD would handle this situation and if there's any significant wear for the clutches in that LSD.
Now keep in mind that OEMs develop these LSDs, AWD/4WD drive trains to tolerate some differences in diameter. For example, I don't think a worn tire vs a new tire of the same factory size is going to damage the system - I would imagine the system can tolerate these very minor differences in diameters.
I think it could be an issue if you have tires that are significantly different in diameters (and this rolling circumference). What exactly threshold is - I don't know.