Iterative experience (experimenting with different ideas, deciding what works best) and speed of execution (once I was happy with it, making it happen required almost no work).
Yes. Even without Claude design and just Claude code, it can use existing design and build out new mockups in-app, which is much easier to demo , tweak and then implement the backend (if any) - all through Claude Code (or Codex if you prefer that). We use both and are now leaning more towards Codex over Claude