I use Github with clubhouse.io. Having a story for tracking the progress of work on a bug automatically move across columns on the kanban board means everyone who isn't a developer knows what the state of it is without needing to learn to use Github and development langauge. It makes talking about the progress of work much simpler.

Essentially I view integrations as a way to automating translating information between developer's focus and understanding of something, a product/project manager's understanding of it, a client's understanding of it, etc. I don't need to explain that a bug has progressed past PR and deployed to a test server if the product manger can see the story move from Development to QA on their view of a project. Also, as people are fallible, it means no one has to manually update the status of a story. Everyone is up to date by 'magic'.