Looking at examples, it's almost always the li tag, mostly for formatting reasons—in html, closing the tag leaves large gaps between lines in a bullet list. (Markdown format does alleviate this.)

... I've also got some saved template posts that used unclosed li and now have approximately a hundred instances of the same tag that need to be closed before I can save any changes to the post, which is frustrating. And if I type li at the end of a line when I meant /li, I end up having to go through all hundred instances of the tag to find the one with the error.

(I did sometimes leave center unclosed, but only once a post, so it's not really much of a hassle to have to close that.)

Thank you for the prompt response!