It actually also removes some advantages. The author fails to point that out, but the advantage of these small steps is that you can roll back to the previous version at any time without loosing writes. If you find a production bug that does not impact data consistency, you can go back one version without loosing the writes that happened while the new version was up.
> To put this in context: say you guarantee 99.9% uptime - that's still 43.2 min / month of downtime available to you!
On the other hand, there might be a fatal bug at some point and you will need 3 hours of leeway to get up & running again. Shutting down is surely the easier method, but the available downtime is usually not free real estate for updates.