The characters that break a link are invisible
A headline written in a word processor does not contain the apostrophe on your keyboard. It contains a right single quotation mark, and the dash is an em dash, and the three dots are a single ellipsis character. All three look normal in the title and all three percent-encode into a URL that is ugly at best and broken at worst when it is pasted into a chat client that stops escaping at the first unusual byte.
Folding accents matters for the same reason. A slug containing an accented letter is legal, but it will be percent-encoded in some contexts and not others, which means the same article can end up with two URLs that a crawler treats as two pages. Reducing it to the base Latin letter gives you one canonical, boring, portable string.
Hyphens rather than underscores, and why it still matters
Search engines treat a hyphen as a word separator and have historically treated an underscore as a word joiner, so my_first_post can be read as one token where my-first-post is three. The practical effect is smaller than it once was, but the convention has settled and consistency across a site is worth more than the difference either way.
The stronger argument is human. Underscores vanish under the underline that browsers put on links, so a reader cannot tell whether a URL has a separator there at all. Hyphens survive, which matters whenever a URL is read aloud, printed, or typed from a screenshot.
What this does not do
It folds accents; it does not transliterate. A Cyrillic, Greek, Arabic or Japanese headline will not come back as Latin letters, because transliteration is a language-specific problem with genuine disagreement about the right answer, and a generic implementation produces results that are wrong in ways their authors cannot see.
If you are publishing in a non-Latin script you have two reasonable options, and picking a tool that guesses is neither: use the script directly in the URL, which every modern browser handles and which readers of that language prefer, or transliterate with something built for that language specifically.