MediaWiki is fine, but at the same time I think the Markdown approach (either with mkdocs or docsify) is superior in most aspects. I like the idea of documentation as plain text files stored in directories in a git repo, instead of a SQL database, it's easier to migrate to other technologies if needed, easier to backup and much more transparent.
I18n is possible if you store files in directories per locale, it's just a matter of convention (i.e having a theme that understands that structure). But I personally never threaded there, need to research a bit.
You can also edit any doc from the GitHub editor just by having a GitHub account. I have seen themes where each document page has a "Edit this page" link, which takes you to the Github edit URL for that specific page, so it's very direct. To simulate the same behaviour of "allow any edit" as in wiki, we could have a Github bot for auto merging those kinds of PRs too.
I can help with this if we decide going back to markdown again (I know it's a lot of work, but maybe some of that can be automated?).
But regardless, I agree with all your points mentioned (I really like that four kinds of documentation post).
It'd be nice to have a guide on how to contribute to the docs too, as @raph said (about adding new entries, updating examples, translating, etc). About translations, I'm not sure if there is a way to show or display all untranslated pages, or see how's the progress of a particular language, but I guess we could be more transparent of the whole process, to prompt more users to translate.