A Rose by a new name
Anyone who has ever employed developers to write apps for their business has been doing this since the beginning. It used to be called Continuous Improvement, integrated with the basic business process itself. If not, why did you employ developers in first place? It's what I still do, day in and day out. You don't need DevOps or cloud, you need good developers to make it work.
Now, at large scale, I can see where that can get tougher. Maybe DevOps helps there, I can't comment on that. But lets not pretend the idea of improving your systems on an ongoing basis is anything new.