I love hearing these kinds of stories just to remind myself how not dysfunctional my own company actually is.

I know plenty of companies that rarely apply any patches or do OS upgrades. I'm talking servers with 4 to 5 year uptimes, still running Ubuntu 16.04 or worse. They don't want to reboot because some dude who left 4 years ago set everything up, often in a non-standard way, and nobody is quite sure how it works. They certainly don't want to be blamed when production goes down. I did a contract job for a very large company that was running a 6 year old distro on a "critical" server and was afraid to do anything beyond changing a password. It's easier to have an outside person do it, so they can blame them when it gets screwed up.

Wouldn’t it be possible to automatically backup the data before reboot ?

Docker offers persistent volumes, so my 30 second solution would be that

That assumes a willingness to learn enough about Docker to understand how you configure your container to do what you want. That can, in some organizations, be too much to ask of researchers. That's the core of the problem.

I believe that was asked for by the SREs- e.g. Tensorflow supports checkpointing to disk and restoring progress- but the ML training software used by the data scientists did not have this feature.