You missed another benefit towards API first development: it makes it much easier to get a head start on mobile development as you can reuse many of your endpoints for common operations.
You bring up a great point. I didn't cover mobile development specifically as we hadn't had a use case for a mobile app yet as the site is full responsive. I opted for more of a blanketed statement in the section on "Developer Liberation" as to how the API covers all client bases equally well.
