From what I've gathered there are two primary functions of the "Cake".
1. Burnout Prevention
2. Flavour
In terms of protecting your pipe, more cake will always be "better", assuming you're worried about tobacco burning too hot. Lots of people aren't, some are, I don't think I've ever seen a warranty stipulate you must have cake on your pipe, so in the end it's entirely your choice.
If you're not overzealous with your cleaning then even a thin carbon layer probably makes a big difference... "Probably", I have nothing scientific to back that up. Most manufacturers use pre-carb at this point as well, so at least we have some precedent for the idea of a thin layer being some kind of ideal (I've never seen a pipe with a 1/8" pre-carb).
The effect of cake on flavour is probably much more important for most people.
As you smoke a given blend in a pipe, the flavor of that blend will be part of the cake.
Wash out the cake and you will lose at least some of that imparted flavor, sometimes called the "Ghost" if it's something you don't like. Given the great lengths people go through to perform an exorcism on their pipes, a simple washing is clearly not going to remove all flavour imparted by the bowl you just smoked, but I'm just guessing it will reduce the effect if it is something you want.
Personally I tend to wipe out my pipes with paper towel after each use.