Makes no sense. It's much cheaper on S3 or even GitHub Pages ($0).
It's not free, that's true. But it's very cheap, especially when paired with Amazon's 1-year free usage tier. But the main benefit is the added control over the web server.
The main benefit you mention is the biggest disadvantage of this solution as you may need to scale it as traffic grows. You can avoid it by using S3/GH Pages.
I actually found that GitHub Pages didn't scale well at all -- during peak traffic, response times slowed to over 10 seconds. This was my main motivation for the switch. Nginx (even on a micro EC2) should be able to handle very high load without the need to scale. S3 is definitely a viable option as well (and I'm not suggesting you shouldn't use it) but I find that an EC2 was a better fit for my needs.