There are all kind of issues with HTML include as others have pointed out
If main.html includes child/include1.html and child/include1.html has a link src="include2.html" then when the user clicks the link where does it go? If it goes to "include2.html", which by the name was meant to be included, then that page is going to be missing everything else. If it goes to main.html, how does it specify this time, use include2.html, not include1.html?
You could do the opposite, you can have article1.html, article2.html, article3.html etc, each include header.html, footer.html, navi.html. Ok, that works, but now you've make it so making a global change to the structure of your articles requires editing all articles. In other words, if you want to add comments.html to every article you have to edit all articles and you're back to wanting to generate pages from articles based on some template at which point you don't need the browser to support include.
I also suspect there would be other issues, like the header wants to know the title, or the footer wants a next/prev link, which now require some way to communicate this info between includes and you're basically back to generate the pages and include not being a solution
I think if you work though the issues you'll find an HTML include would be practically useless for most use cases.
The include logic of include2.html missing everything else would also apply to all other includes.
If a user clicked a link with src="include.css" then it'll be rubbish.
It would be good for static data.. images, css, and static html content.
These are all solvable issues with fairly obvious solutions. For example:
> If main.html includes child/include1.html and child/include1.html has a link src="include2.html" then when the user clicks the link where does it go? If it goes to "include2.html", which by the name was meant to be included, then that page is going to be missing everything else. If it goes to main.html, how does it specify this time, use include2.html, not include1.html?
There are two distinct use cases here: snippet reuse and embeddable self-contained islands. But the latter is already handled by iframes (the behavior being your latter case). So we only need to do the former.