① The trailing slash doesn’t make a tag self-closing. All it does is get ignored, emitting a parse error (which in common compiler terms is just a warning) if you use it on a non-void tag.
You can’t use <div/>. You can’t use <custom-tag/>. The only tags you’re allowed to use the trailing slash on are the defined void tags like <img> and <br>.
It’s not “not necessary”, it’s “completely useless, by definition”.
I’ve seen people presume they can close tags this way. JSX probably helps cause this, because you can there. But because self-closing tags aren’t a thing in HTML syntax, I think it’s harmful to use the spelling at all in HTML syntax.
② I wouldn’t mind so much if people used it consistently, and I wouldn’t mind at all if it was being used to support both HTML and XML syntax, but if you see sites that use trailing slashes on void tags in their head, practically every time there will be at least one tag that isn’t using it:
<link … />
<meta … />
<link …>
<link … />
③ I also dislike it because it’s fairly common for syntax highlighters or other casual parsers to get it wrong. Most commonly, I’ve seen tools misinterpret an unquoted last attribute, treating <a href=/example/> as <a href="/example" /> rather than <a href="/example/"> before. (Same with the likes of <img src=/example/>, but anchor hrefs are more commonly going to look like that.)I have never heard of anything even vaguely matching your description, and it would be wildly wrong. HTML parsing is exhaustively defined, and the only way of correctly parsing HTML is to use the defined HTML parser.
xhtml still works in modern browsers btw. It's still probably the easiest way to do page templates. XSLT shows its age without the ability to modify the page after load (unless you run it via javascript), but we could've just added that and it'd be almost perfect.
I personally prefer having the /> even though it's not necessary, so that I can tell at-a-glance whether a tag is self-closing or not. It doesn't hurt, does it?
(plus I'm just used to it because the book I learned HTML from was confident that XHTML was the future)