The problem with wadding, as I see it, is that there is ALWAYS a chance that your finger is protected by only ONE ply!
With folding, you are protected by at least two; and up to 14 plys (I am told you cannot fold paper more than seven times).
Folding also allows for adjustment of thickness based on diet.
For example;
If I had dined exclusively on high fiber foods and cheese, one fold will suffice.
If I had dined on sauerkraut, bean, jalapeno and butter casserole, then four or five folds is a good idea for maximum protection from potential caustic material.
just my $0.02.