alt Hacker NewsTrue, a very simple analog circuit would be enough.
However the bane of analog circuits was that they age, so a control circuit that works perfectly today will drift and no longer work as intended after some years.
The second problem is that analog circuits need adjustments to set them at the exact desired parameters.
Adjustments can be done either by using an adjustable element in the circuit, e.g. an adjustable resistor or capacitor or inductor, or by measuring many resistors and/or capacitors and/or inductors and selecting the ones with the right values to be used by your device.
Redoing periodically the adjustments also solves the aging problem. However, both the initial adjustment and any periodic readjustments need a lot of work, so they are no longer acceptable in the industry.
When doing something for yourself, you may make an analog controller and the initial adjustment would not be a problem, but even in this case it would be annoying to keep track and remember something like having to readjust a fan controller every 6 months, to be sure that it still works as intended.
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Analog control circuitry is also really hard to patch in production, or to adjust to different behavior during design.
Oh, you need a quadratic fan curve instead of a linear one? Have fun starting from scratch!
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.