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.
It's possible your definition of mission critical just doesn't match up to that of those responding to your comment.
If the loss of a set of data would threaten the existence of the company, that's mission critical. While having a sophisticated niche tech partner handle day to day operations of that data is one part of managing the risk of data loss, if one put all their eggs in only that one basket, that would possibly indicate one has a lack of experience with tech vendors and hasn't read anything about managing risk.
Every business should have at least one routinely tested, independent path for mission critical data recovery.
I think you're right. But I also do not think Purelymail falls in the same camp that Fastmail or Office 365 do, so far as expectations of reliability and business continuity are concerned.
The broader question of whether it is appropriate to independently back up your own data in large scale cloud services need not be answered. It is simply sufficient to recognise the risks are far greater when dealing with a one man operation.
Why would I lose access to my Fastmail account? That risk is a remote one. I have 2FA, they take backups and provide support, and they are a reliable company (at least, not a one-person operation).
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.