Yes, yes, but they will notify you after your service is down (because that's when they notice), in part thanks to a spacer file that eats up available disk space without being of any use. A monitoring service would notify you before your service is down, users grab pitchforks and start looking for torches.

I understand the benefit to be able to quickly delete some file to be able to run some command that would need space, though I find that highly theoretical. If it's your shell that requires space to start, you won't be able to run the command to remove the spacer, and once you're in the shell, I've never found it hard to clean up space; path autocompletion is the only noticeable victim usually. And at this point, the services are down anyhow, and you likely don't want to restart them before figuring out what the problem was, so I don't see the point of quickly being able to make some room.

It feels like "having two flat tires at the same it is highly unlikely, so I always drive with a flat tire just to make sure I don't get an unforeseen flat tire". It's cute, but I'd look for a new job if anyone in the company suggested that unironically.

This is an additional safety net. It's like doing backups. Of course you should replace your hard drive before the other drive breaks down, but you want to have a backup in case your server burns down.