The "coolness" of the URI is measured by how non-changing it is.
Including ".html" in the URL when you're first creating a site signifies a risk that it'll change in the future, because it's evidence you went along with what was easiest to get the backend technology to serve your content, and as the backend changes over time, you'll do that again, changing the visible URI as you go and causing bitrot.
But if you picked ".html" and stuck with it, that's now the cool URL, and you should use web server configuration to make sure it remains that way, even if the backend technology has changed completely.
For an extreme example, when eBay started, everything was cgi.ebay.com/ws/ISAPI.dll?ViewItem=blah (or something like that), which has many specific technology implications! But it stayed that way while they changed out all that technology over the years. (I see that now they’ve gone more abstract, though.)
Including ".html" in the URL when you're first creating a site signifies a risk that it'll change in the future, because it's evidence you went along with what was easiest to get the backend technology to serve your content, and as the backend changes over time, you'll do that again, changing the visible URI as you go and causing bitrot.
But if you picked ".html" and stuck with it, that's now the cool URL, and you should use web server configuration to make sure it remains that way, even if the backend technology has changed completely.