I don´t think that design is a service. It can be sometimes, but service doesn´t define a design, because a design can also have an expresive aim.

Now, in the case that design is to serve, I think that the concept service means a contribution, a help, but not just for the one that a designer work for. A design can serve a cause or an idea, even serve the world. To serve is to do a design for and to an aim that is not yourselve.