Serving a website from Amazon S3 is great: it’s fast, it’s inexpensive, and it doesn’t require maintaining a web server. But this simplicity can be limiting, coming at a price: you can only serve absolutely static files; there is no server-side logic whatsoever.
On the other hand, we are now seeing the rise of so called “API-first content management systems.” These systems, in true cloud spirit, are usually provided as a hosted service, give you a standardized user interface for structuring and managing your content, but do not deal with any aspects of your content presentation. They don’t deal with themes, templates, pages, etc. Instead, you have a fast and simple RESTful API that gives you access to your content and you are free to render it with whatever presentation you want outside of the CMS.