If the issue is that "include" somehow makes it sound like it's not markup, the solution seems obvious. Just use the src attribute on other tags:

<html src="/some/page.html">, <div src="/some/div.html">, <span src="/some/span.html">, etc.

Or create a new tag that's a noun like fragment, page, document, subdoc or something.

Surely that's no less markup than svg, img, script, video, iframe, and what not.