I feel like you're making two somewhat contradictory arguments. The first is that this is inconvenient in several specific situations. The second is that passwords aren't a problem because people should use password managers. But the specific situations you mention are exactly the situations I've encountered in the past where my password manager isn't available either (which you acknowledge).

I do agree though that these are real problems. One advantage of using short-lived random keys for the emails is they could be short enough to manually enter (shorter than a secure password). Obviously you'd need to implement rate-limiting on the login page to prevent people from brute-forcing outstanding logins.