Heroku doesn't actively prevent you from hosting a static site. Yeah, heavy assets like images and video should be hosted elsewhere, but with HTML and stuff it's fine to just throw it in a static Git repo and use Heroku.
The main thing that will stop you is the limit on the "slug size", which is 100mb. This is heaps for static text like html, but if your blog is image intensive you could hit the wall after a while. Video would push you over super quick.
