One of the main problems with many non-wax lubes is that sand and grit adheres to it, which makes a grinding paste. Then, when you clean the chain, the finer particles get washed into the roller surfaces, so even though it can look clean after an organic solvent wash, the grit continues to do damage.
I don't think wax is immune to that, but grit doesn't adhere to it nearly as much, so less is present when it comes time to re-wax.