I think the reason it doesn't wear out is that it is only having to work against a very small speed differential between the input and rear wheel speed which as we have discussed is where most of the torque is going anyway.
It is not like you Exedy

trying to make up thousands of RPMs of differential at max torque.
I think the heat is more likely coming from the LSD clutch, but could be mistaken. I can't remember which clutch pack has more surface area. Whichever it is, that's the one making the heat.