That's what most people think and so did even John Currie years ago but he and the rest of the aftermarket axle/gear industry no longer think that way about synthetic gear lubes.
Aftermarket axle and R&P gear providers started seeing an upturn in problems. For one good example, Currie builds axles and installs whatever ratio aftermarket gears the customer wants. They had a normal warranty repair rate until they started seeing a climb in warranty problems. It became alarming enough that they started examining all of their processes and parts to see what was causing the upswing in R&P gear failures. All of this is right from John Currie, I personally heard him explaining what they saw and what other aftermarket axle and gear manufacturers started seeing.
They found nothing in their processes or in their supply chain to account for the rise in R&P problems. They noted the failed R&P gears they were receiving back showed signs of being overheated. Looking into the overheated gears their customers assured them they had been carefully broken in with short trips, cool downs, etc. Currie was stymied. Then they figured out from talking with the customers with the failures that the only commonality between them was those with failures had broken the gears in with synthetic gear lubes. That confused everyone since like everyone else they didn't believe the synthetic gear lubes could be the cause.
They used IR heat guns to measure the diff covers and the temperatures were lower at the diff cover when the lubricant inside was a synthetic vs. higher diff cover temperatures with a conventional gear lube. That totally shocked them, how could the covers be cooler with a synthetic gear lube yet the gears lubricated with synthetics showed clear signs that they failed from excessive heat during the break-in process. John made a big point that they and the aftermarket industry members they consulted among were blown away by what they were seeing. It was clear the gears were failing from heat at a higher frequency when lubed with a synthetic but the diff covers were cooler showing the conventional gear lube was cooler. They were totally confused at this point.
Currie then resorted to building a special test jig/axle so they could directly measure the temperature of the gears themselves, not the gear lube just behind the diff cover. That's when they discovered the shocking news that even though the synthetic gear lube itself was cooler, the gears themselves were much hotter! Switching to a conventional gear lube, they noted the gears ran much cooler in the test jig with the conventional gear lube. They determined, and this again is right from John Currie's mouth, that the synthetic gear lubes were not sinking/extracting the heat from the gears as well as the conventional gear lubes did... which is why the conventional gear lube and the diff covers were hotter.
John then said once they changed their warranty to require the use of conventional gear lubes that their gear failure rates dropped back down to what they considered normal. Dynatrac had the same results. It was about this time when aftermarket gear manufacturers like Revolution Gear and Yukon started recommending the use of conventional gear lubes during the critical break-in process. For one example Revolution says "Recommended gear oil is an 80W-90 or 85W-140,
Non-Synthetic, GL5 grade or Higher" at
https://www.revolutiongear.com/ring_and_pinion_break_procedure
And again, I let myself get talked into using a synthetic during the break-in of my new 5.38 gears even though I had already bought the conventional gear lube. And toward the end of my VERY careful break-in the rear axle's gears started howling. The gear "guru" guy I took my TJ to have the new replacement gears installed removed the old gears and immediately accused me of "stupidly" having used a synthetic gear lube, he said the gears showed signs of significant overheating during the break-in process despite my anal/careful break-in with lots of cool downs. He pumped in conventional gear lube afterward and I went home and changed my front axle back to a conventional gear lube and that's all I have ever run since.
Why can our factory axles run fine with synthetics with the gears the factory installed? Because the Spicer gears the factory installs come thoroughly pre-lapped and don't require a break-in. All aftermarket gears require a break-in in so while some will instantly say they had no problem breaking their new aftermarket gears in with a synthetic, I'll just say good for you and that you obviously were very lucky.
Sorry for the long comment on this but my experience with my burned-up RGA gears with a synthetic gear lube matches what I heard John Currie saying years ago together. That plus aftermarket gear manufacturers recommending conventional gear lubes and my personal experiences taught me to stick with conventional gear lubes for my aftermarket gears. Hate me all you want for what I wrote above but I really don't care. Run what you want. If what I wrote here saves one set of new aftermarket gears for someone here it'll make my day.