You're over thinking it. If the application is very simple and needs to do one thing, an analog system works fine. Once you start needing sequencing, multiple adjustments, and maybe a little smarts then a CPU can get involved.

I worked at a shop that had an old closed loop water-air chiller for a laser. The water temperature controller was a small PCB with an op-amp chip with some passives and the temperature was set by a potentiometer. That thing ran fine until the compressor died and it sent to scrap.