Comment by dwheeler

HTML was historically an application of SGML, and SGML could do includes. You could define a new "entity", and if you created a "system" entity, you could refer to it later and have it substituted in.

    <!DOCTYPE html example [
      <!ENTITY myheader SYSTEM "myheader.html">
    ]>
    ....
    &myheader;

SGML is complex, so various efforts were made to simplify HTML, and that's one of the capabilities that was dropped along the way.