This second approach is a variation on the theme, but this time you might think you have solved the first problem but in reality, you have not. We have mapped and modelled hundreds if not thousands of processes in our time. The most important element by far from a learning perspective is the capture of the As Is process (the current state). We believe the most important people to be in that workshop or workshops is the people doing the work. They have the most to give and the most to learn from the knowledge of how the end to end process currently works across silos.
This approach is all too common in our experience is to look to improve the end to end process. The knowledge and understanding of the end to end process is only gained by the business analysts. The other drawback of this approach is the lack of buy in by the stakeholders. Because they have not seen or understood the end to end process, they cannot help shape the solutions and nor are they very likely to buy in to the end results. Have a look here at how Toyota develop capabilities and focus on learning (this is hot off the press and the first time they have covered the topic also it was tweeted by Daniel T Jones) https://planet-lean.com/lean-learning-toyota/