If the issue is that "include" somehow makes it sound like it's not markup, the ...

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.