I think the design issues for APIs, DSLs and languages are very similar.
For adoption, the learning curve is very important, and the beginning of this curve is sensible defaults (like Python and Rails), so you can make the common tasks happen fast, while having the power to also do the complex low-level fine-tuning that is less common (and not the first thing you do). There's a learning curve (per user), but also a building curve (per project).
However, common is an attribute of usage, and not intrinsic to the API. You need a lot of users before you know what is common. And, over time, as the world changes, the common tasks change (eg. there are many different internet protocols, but http turned out to be most common).
