I already spend all my time in the inbox and find it hard to ignore an email. Inbox zero habits would kick in and ensure that I do at least some memorization every day. A single Anki card in my inbox is far less daunting than the entire deck staring at me when I open the app.
Unfortunately Anki doesn't have a proper API and isn't easy to reverse engineer. I tried to build something using a scraper that logs in to the Anki web app, but it turned out to be very janky, and couldn't identify overdue cards. Somebody with better desktop app/python skills could probably do it locally, but I gave up.