This is such a remote possibility, at least with Fastmail, that I do not consider it reasonable to implement my own backup solution. If they are going to shut down, it isn't going to occur imminently and without any warning.

It's an easy statement to make: "just take a backup". But that requires me to dedicate time to implementing a secure and automated solution (and of course, routinely testing restoring it). I'm not doing that, because I pay the service to do that for me. If I'm going to that effort, I may as well self-host.