GitHub is indeed production ready. They use replication, clustering and load balancing to provide low latency and hight availability and I would say they are pretty good at doing that. You can have an idea about the latest issues by reading the status page.
However, they aren't a real hosting. Compared to Amazon S3, for example, Amazon provides the following advantages:
- An infrastructure about order of magnitude bigger
- Ability to use CDN (Amazon CloudFront) to reduce latency by serving the pages with the nearest node according to user's location
The advantages of using GitHub pages is normally for Ruby users that wants to use Jekyll (the tool behind GitHub pages) and wants to leave GitHub the effort to compile and host the site. Last but not least, it's free (as long as you keep your repository public).
But nothing prevents you to use Jekyll locally (or any other publishing tool), generate the pages statically and host them on Amazon. I'm doing this for several projects. There are several command line tools to sync your local copy with the Amazon folder.