Take Sisyphus. Who, or what, does his task serve? Himself? Someone else? Something?
1/ The output of the job is not obsolete, otherwise, we wouldn't even run a machine to produce it. So the machine needs to be maintained/worked on, it turns out. Only the maintenance job may also be way more boring/soulless that the actual task given to the machine. Without maintainers, the machine is nothing.
2/ The "meat" of the job/activity may still be of higher interest for the person doing it. If I enjoy doing something, can it ever become obsolete?
3/ The same "meat" of the job, or even its output, may ever be significant only if a human does it (art is interesting _because_ it is produced by someone/a human I can relate to, because it _says_ something I can relate to - otherwise, it becomes as tasteless as a chewing gum after some time).
4/ The income/consequence a person gets in return for her job is not obsolete either. Only the one with the money/capital found a more affordable way of getting it done - but economically in the short run, only - it may very well have higher order consequences that happen to make the move more costly - but still it depends what game one is playing - if short-term benefits is all you play, you're definitely fine.