For three hundred years people were able to run them furnaces without the aid of computers just fine. But after the 'puter takes over, you can't do anything without it, even if the damn thing goes south... I'd say it's not a very good design.
If by "just fine" you mean having a small fraction of the throughput of the modern machinery. The automated systems can be (and thus are) run at damn near peak capacity at all times, which means that when they do fail, it will inevitably be at the worst possible time -- because it's always the worst possible time. The trick lies in determining whether this increased cost of failure is offset by the increase in production. From the widespread adoption of such processes worldwide, it would appear the answer is a resounding "yes".