Ironic, the day after the launch of Artemis II that people are using microcontrollers far more powerful than the original Apollo 11 navigation computer to control a single fan in their PCs now.
I went through this years ago making a fan driver for my vehicles HVAC blower. The analog setup was fun to make but you use more board space, higher BOM count, and really, higher BOM cost vs a micro-controller.
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.
Oh, you need a quadratic fan curve instead of a linear one? Have fun starting from scratch!
My point was that, if you want additional behavior, you need to bake that in from the start. With an MCU you can trivially switch it in-the-field to literally anything you can imagine.
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.
It's not just a dumb fan controller that I could've bought off aliexpress.