I think this is a fabulous idea. I would, however, add that, sometimes, customers want to know when things will get delivered, so some form of estimation may be required.

In implementing what you described here, I might need to also ask the team to relatively estimate each 'narrative' either in terms of story points or ideal weeks. This serves not only to set delivery expectations, but also allows us to compare value with the effort to deliver it and therefore development and delivery sequence.