It would be helpful if you could give an example of an application or a pattern where such a technique of distinct routines to handle different arglists would be useful.

Here's an easy one off the top of my head:operator overloading. Not often done, but useful. You would, for example, want to handle multiplication differently if the left and right sides of the * were both matrices then you would if the left side was a matrix and the right a scalar. (In the first example you'd probably do a full matrix multiply, and in the second you'd probably multiply each element of the matrix by the scalar. Probably...)

Any time you have a sub that checks the passed parameters and then dispatches to different code depending on the type or quantity of the parameters you're a good candidate for this. It's much less error prone (and usually faster) if the language handles the dispatch.