I use Github Pages to host a small static site created with Publii. This site is visible at http://myrealbook.vintherine.org/. For a static site that does not ask for any login, without contact page and allowing no comment I did not find useful to worry about HTTPS.
The problem is that if the address is forced in https the page is displayed but without any style. This is for example the case with Firefox in private window (even if the option “Do not activate https mode only” is checked).