This is because of a shortcut that somebody took when building your server originally, by failing to make the deployment reproducible.
> ...where one of the packages I relied on suddenly became unsupported
I've never heard of this happening in any Linux distribution. Can you be more specific? Did you choose to use some third party source for a package here? If so, how can you expect your distribution's developers to support you going off-piste in a way that they never claimed to support in the first place?
> Old, dodgy, out-of-date servers exist exactly because updates are butthole-puckering, because everyone's been burned at least once by a "minor" update, and because once the damage is done, undoing it is horrifyingly difficult.
You might want to look into "DevOps". The idea is that you script your deployments together with automated tests for them. There are many tools to help you do this now. With this in place, nothing you've stated is true any more.