My two cents

A marketing approach is really great to focus on how people will hear about your service and how they will join it. A service design approach takes into account these moments but then continues to explore how to help people get the most of the service and even help them leave it.

We can easily mix both approaches by adding the steps of a classical marketing or purchase funnel (Awareness, Interest, Desire, Action) to the classical structure of a Service Blueprint (Aware, Join, Use, Develop, Leave).

If we do that, we basically, zoom in on the "Aware" stage of the service blueprint by adding some more steps inspired by the purchase funnel. This can give us the following structure for our blueprint:

"Awareness, Interest, Desire, Action, Use, Develop, Leave"