Dumb question about AWS vs "simple" hosting

I'm trying to figure out the advantages of using AWS vs a "simple" host like Hostgator. Running a "small" Linux EC2 instance costs about $63/month, while Hostgator is like $5/month.

I'm just trying to host a small website/blog. AWS is probably overkill for this purpose, right? (I've installed Apache/PHP/MySQL etc. on a local VM before, so I'm not afraid of tech problems.) The only advantage AWS offers is the flexibility it offers in what you install in the instance, correct?

Thanks!