In general, you've hit the high points yourself.
The benefits (and issues) will vary by post model, manufacturer, and design. Carbon fiber is a very versatile material engineering wise.
Storck makes 2 carbon posts, which are externally identical. But one is a comfort post, which focuses solely on smoothing out your ride, and the other focuses on being light and stiff.
While there were issues with catastrophic failures, especially in early models, carbon component design is no longer in its infancy, and you are extremely unlikely to have failure issues if you choose your components and ride in a manner appropriate to the style of bike you own.