The reasons I heard for using the wads:
Recommended by maker. Full stop.
So I follow.
As for the background of this, I heard two explanations:
1. Greasing the ball while fired. Cleaner barrel during continuous firing.
Prevention of chain fire. What I heard, back in old days the chain fire was not uncommon. They were using powder, balls and caps. Casting their own balls in the field (questinable quality and dimensions), and probably the chambers in cylinders were not sealed properly - which resulted in occasional chain fire. The quality of hand made bullets in old days coud be different when compared to modern ones.
So, in modern replicas where modern makers try to avoid injury claims - they recommend two things: wads - to place a layer between ball and powder, and in this way prevent a spark triggering next chamber.
And, two, they recommend some lubricant on top of chambered ball - for same reason - to prevent unwanted spark entering next cylinder chamber.
Apart from safety, cleaner barrel is also the outcome.
Despite the recommendation, I tried both ways. I did not notice any difference in accuracy: when using traditional load (powder, ball, cap) or modern load with both additional ingredients wads and lube.