alt Hacker NewsI know it’s not straight HTML, but SSI (server side includes) helped with this and back in the day made for some incredibly powerful caching solutions. You could write out chunks of your site statically and periodically refresh them in the server side, while benefitting from serving static content to your users. (This was in the pre varnish era, and before everyone was using memcached)
I personally used this to great success on a couple of Premier League football club websites around the mid 2000s.
One benefit of doing it on the client is the client can cache the result of an include. So for example, instead of having to download the content of a header and footer for every page, it is just downloaded once and re-usef for future pages