As it turns out, Google is not sufficiently convinced that I am in fact the owner of the account, so it refuses to let me download the data. I don't feel inclined to spend time trying to figure out this nonsense, but thankfully none of the information in that account is particularly important. I'll take it as a sign that I should just move away from Google, because next time the information on an account could be actually important, and I'd be screwed.
First, getting to a point where you can actually schedule the creation of a zip takes a lot of clicking around - just to make sure that people won't bump into it unless they're explicitly searching for it.
Second, the process is painfully slow (on purpose). Last time I used it was to download my YouTube subscriptions and playlists to import them into my Piped instance. Even though I only have about 100 subscriptions, and only two playlists with about 20 items each, the process took almost two days to complete. By then I had already made a script that scraped the content from their HTML (and it only took me 5 minutes), and another one that did the same but using the YouTube API. If it takes less than a second to get the playlists and subscriptions of a user, I don't see a single reason why generating a Takeout CSV with the same information should take 2 days. I was determined (and tech-savvy) enough to script my way out of it, but many users just get discouraged and give up the idea of exporting their Google data entirely.
> Automatically create an archive of your selected data every 2 months for one year. The first archive will be created immediately.
While I was waiting on that, I finally paid for a proper email service and migrated my domain, so I have a copy of my Gmail data and a working, Google-free email service now.
It's been unreliable for years.