- You can't update your blog unless you have a computer with the right toolchain available. That includes uploading a cute photo from your smartphone.
- You can't do delayed posts.
- You can't have local comments (you can have disqus or similar, but then comments aren't part of your page, and won't show up in searches). Pingbacks won't work.
- You probably don't need fast. Wordpress + WPcache is really fast.
If your static site does any of this, it's not static, it's a dynamic site that uses the filesystem rather than a DB for storage -- which might very well be clever, but that's not what's being argued.