Hi Robert,
Welcome to ETO. I see you are from the States, which one. If you put it next to 'Location' on your user page it will show in the panel on the left of your posts.
Theoretically an interesting approach, but there are a number of issues:
(1) Why use Pulse Width Modulation (PWM)? The fan is either on or off; fan speed control is not required.
(2) The OP has no experience of electronics, let alone microcontrollers
(3) PWM is a higher risk, especially as we do not know the characteristics of the fan.
(4) Electromagnet compatibility (EMC) could be a problem
(5) Snubbing would be more critical
(6) The MOSFET would be more vulnerable, more critical, and more expensive
(7) You would need an extended temperature range microcontroller
(8) The microcontroller would need a program, implying an integrated development environment (IDE) and host
(9) The microcontroller would require a stabilized supply line (5V or 3.3V)
(10) By definition, the reliability would be less
(11) The cost would be higher and component availability would be worse.
(12) Susceptibility to electrostatic discharge (ESD) would be worse.
(13) The MFC would be more susceptible to moisture
(14) The relay provides isolation between the blood and thunder of the fan circuit and the decoupled supply line for the Schmitt trigger. A MOSFET controlling the fan directly does not do this.
By the way, I did consider driving the fan directly with a MOSFET, rather than a relay, but decided against it on the grounds of risk and reliability: switching fans with automotive relays is universal and well proven.
spec