The problem with using Heroku to host a static website is that it is the kind of thing that you can technically do, but probably shouldn’t. One reason is that it adds an extra level of maintenance requirements on you. You have to worry that whatever programming language and server software you are using to run the site are supported by the Heroku platform, and that you keep them properly up to date.
You have to download a bunch of tools that allow you to simulate the Heroku stack in order to ensure that your website will deploy and run properly.
Your site is deployed to Heroku by pushing your code to a Heroku-hosted Git repository. If you want to take advantage of the benefits of a platform like Github or Gitlab, you will have to make a mirror of it on one of those sites, and keep it updated as well. One more step in the publishing process that honestly isn’t necessary.
If you want the site to load instantly for users, you need to install some Heroku plugins and tweak them so that your site never goes to “sleep” and is able to serve requests immediately.
Long story short, a service like Heroku is a bit too heavy duty for a static site, and requires more work than I am (and I imagine most people are) interested in taking on.