Is this because WordPress knows no such thing as a taxonomy archive index page? My understanding is, that is not a thing. Hence, I wrote page-events.php as a page template, and the code content spits out the relevant queries to list the terms.
Yes. All frontend pages in WP are post queries. WP looks at the query to figure out which template to load, and the main loop displays the posts.
If the query is for a single post, then it’s a singular query, e.g. a blog post, a page, etc. If multiple posts are shown, it’s an archive.
As a result, WP has no concept of an archive of users, or an archive of terms. The reason you don’t see the page for the taxonomy itself is because there isn’t one. you can test this out by taking example.com/taxonomy/term and removing /term, you’ll get a 404 or redirected elsewhere.
Likewise, if we look at how rewrite rules work, URLs match on to regular expressions, that turn the URL into a list of query variables for a WP_Query object. The entire URL parsing stack is built to fuel post queries.
Having said that, you could build such a page, but you would need to create a rewrite rule for each taxonomy root page, and add query variables, then look for those and load the template manually, it’s not for the faint of heart. To add to that, these “virtual pages” won’t show up in the menu creation UI.
Keep in mind that in the next year or two, the menu creation process is earmarked for significant change and overhaul as part of the full site editing project, especially with the recent introduction of nav menu blocks ( written in 2020 )