If you're truly running a static site, you can run it for free, no matter how much traffic you're getting.

Github pages is one way, but there are other platforms offering similar services. Static content just isn't that expensive to host.

THe troubles start when you're actually running something dynamic that pretends to be static, like Wordpress or Mediawiki. You can still reduce costs significantly with CDNs / caching, but many don't bother and then complain.