STP is not a lubricant, it is a viscosity modifier[whatever that is].. Personally, I don't want my viscosity modified.. When I was young we did have a number of vehicles come back[ Fords,,, no Studebakers] with defective center mains from lack of lubrication appearing to be from the STP.. We never really recommended its use, regardless of what Studebaker wanted, but some customers wanted it..STP was about the only thing I ever found wrong with Studebaker, hehehe.. A few similar instances occurred when Slick 50 first came out[ we never sold or recommended that crap but some customers would add it]..
As far as adding STP to our tail ends or transmitters, I doubt it would hurt much as long as it was added within reason[ the less the better].. I find they operate just fine however with plain ole 140 wgt. In fact, it appears to me that they seem to be happier downshifting when using the lighter oil, but, that may just be my imagination..