I wonder how they came up with the non-synthetic requirement
I've known synthetic oils to transfer heat significantly better than conventional oils as thermal conductivity typically scales inversely to particle size in heat transfer media
Lots of industry people used to think that too but they no longer do. Buyers of aftermarket axles and gears started having lots of aftermarket ring & pinion failures and companies like Currie and Dynatrac were losing a lot of $$$ replacing them. They then tracked the failures down to the customers who had filled the axles up with synthetic gear lubes. That confused the hell out of everyone.
They started running tests to figure out what was happening. IR guns were showing the pumpkins filled with synthetic gear lubes were running at lower temperatures than axles filled with conventional gear lubes which confused them even more. Probes placed in the synthetic gear lube confirmed it was operating at lower temperatures. It just wasn't making any sense.
They then built a special test jig so they could directly measure the temperature of the new aftermarket ring & pinion gears themselves while lubed with synthetic then conventional gear lubes. Those tests confirmed the R&P gears lubricated with a synthetic were running significantly hotter and the reason the synthetic gear lube was not nearly as effective at sinking/extracting the heat out of the gears as conventional gear lubes were. It shocked the industry experts.
Companies like Currie and Dynatrac then changed their warranties to require only the use of conventional gear lubes and placed tags on the axles indicating that only conventional gear lubes should be used. That stopped the excessive R&P failures. All this happened probably 15+ years ago and I heard about it personally from John Currie.
And when you bring up the fact that many new car axles, maybe even Jeep now I don't know, come pre-filled with synthetic gear lubes yes that is true. And the reason those new R&P gears don't fail is because all R&P gears new car and Jeep manufacturers install are pre-lapped by the gear manufacturers like Dana-Spicer. Pre-lapped means they don't need to be broken in, they went through a break-in/lapping process as a matched pair before being shipped to the car manufacturer and are ready to go as-is.
Aftermarket gears are not pre-lapped and require a careful breaking in process and anything to minimize the heat generated during the break-in process will help them survive that process. The use of conventional gear lube during that critical time is an important part of the break-in process that helps significantly.
Is it possible to install aftermarket gears and use a synthetic during the break-in? Of course, but that places a huge amount of extra care and time required to ensure the gears never get hot enough to damage them during the break-in which is a lot more difficult. I personally had a set of new R&P gears go bad from having used a synthetic gear lube during the break-in. And I took great care during the break-in process to do as advised, I was very careful yet they still got too hot. When the gears went bad and I went to have them replaced, the gear expert I used pulled the gears out and after looking at them said I had "burned them up" and then said 'you used a synthetic gear lube didn't you'. He also confirmed their setup was fine and not the reason for the problem. I learned a huge lesson from that and I do my best to let others know about the recommended use of a conventional gear lube for breaking new gears in so others don't burn their gears up like I did.