But I do agree the poster should think about this. I don't think it's 'off' or misleading, they just haven't encountered a hardware error before. If they had one on this single box with 30 databases and 34 Nginx sites it would probably be a bad time, and yes they should think about that a bit more perhaps.
They describe a db follower for cutover for example but could also have one for backups, plus rolling backups offsite somewhere (perhaps they do and it just didn't make it into this article). That would reduce risk a lot. Then of course they could put all the servers on several boxes behind a load-balancer.
But perhaps if the services aren't really critical it's not worth spending money on that, depends partly what these services/apps are.
Could I take it down for the afternoon? Sure. Or could I wait and do it after hours? Also sure. But would I rather not have to deal with complaints from users that day and still go home by 5pm? Of course!
Also, in general, you can architect your application to be more friendly to migration. It used to be a normal thing to think about and plan for.
VMware has a conversion tool that converts bare metal into images.
One could image, then do regular snapshots, maybe centralize a database being accessed.
Sometimes it's possible to create a migration script that you run over and over to the new environment for each additional step.
Others can put a backup server in between to not put a load on the drive.
Digital Ocean makes it impossible to download your disk image backups which is a grave sin they can never be forgiven for. They used to have some amount of it.
Still, a few commands can back up the running server to an image, and stream it remotely to another server, which in turn can be updated to become bootable.
This is the tip of the iceberg in the number of tasks that can be done.
Someone with experience can even instruct LLMs to do it and build it, and someone skilled with LLMs could probably work to uncover the steps and strategies for their particular use case.