<iframe> is different from what the author is asking for, it has its own DOM and etc. He wants something like an SSI but client side. He explains some of the problems right after the part you cut off above

"We’ve got <iframe>, which technically is a pure HTML solution, but they are bad for overall performance, accessibility, and generally extremely awkward here"

Iframe is stuck in a rectangular box. It's not really suitable for things like site wide headers, footers and menus.

While I get your point, headers and footers and menus tend to all live within rectangular boxes.

Headers and their menus are often problematic for this approach, unless they are 100% static (e.g. HN would work but Reddit and Google wouldn't since they both put things in their header which can expand over the content). I.e. you can make it transparent but that doesn't solve eating the interactions. The code needed to work around that is more than just using JS to do the imports.

Headers and footers, yes. Menus generally need to expand when you interact with them, especially on mobile.

Do a drop down list of links on a header in an iframe