You don't want a PSU fan to stop spinning... I've had the fan controller chip go out in a PSU back in the day and the PSU got extremely hot like an oven before the BIOS detected high temp and shut the system off. I ended up replacing those fans that were connected to the chip with 80mm case fans, running the power connecters out with the PSU power connectors. It's still working fine to this day, surprisingly.
P.S. If anyone decides to replace their PSU fan, be sure to discharge it before breaking it open, know that the charge can be potentially lethal.