I've mentioned in the past that grease and lubrication experts say that too much grease or gear lube can be nearly as harmful as not enough. Here's an example:
A major manufacturer of self-propelled sprayers notified its dealerships of the "fix" for a problem with the final drive hubs on their sprayers overheating. The solution? It was recommended that if a customer complained of overheating hubs, that the dealer should simply drain the gear cases and refill them to a lower level with synthetic gear lube.
Lubricant in gear cases is cooled by being slung onto the gear case walls by the spinning of the gears. As the lube drains down the wall, it exchanges heat with the metal. The larger the air space above the gears, the more opportunity for lubricant to exchange heat and cool the lubricant. It's always a calculated balance to provide enough lube so the gears are well lubricated, but with enough air space to provide adequate cooling.
Synthetic gear lube tends to build less heat, and degrades less if the lubricant runs warmer than expected. Synthetic lube generally isn't "factory fill" because gears "break in" better with conventional lubricants. But once the gearcase has been run, synthetic oils run cooler, with less friction.
It's always best to fill gearcases to recommended levels with recommended lubricants. But this situation proves that when it comes to lubrication, more is not necessarily better.