1 year later and it looks like httpd now supports setting hsts headers, but not expiry/cache-control headers. It looks like the recommendation is to put relayd in front of httpd to set custom headers. That isn’t very appealing to me.
It also seems that there is no current plan to add support for http/2. I can live without http/2 for a while though to be honest – however it IS nice that nginx, which I currently use to serve my static site, supports it.
So httpd has certainly gotten closer to meeting my needs, but still not quite there. I will continue to keep an eye on it though!