OK, then here's another idea to try. Go into BIOS Setup to where you configure the CPU_FAN header. Look for a choice of the MODE it uses - that is, the methoid of controlling fan speed. Often you have choice of Auto, PWM, or Voltage (aka DC) Mode. Try setting it to Voltage Control Mode (aka DC Mode), then SAVE and EXIT. I do not expect this to work, but it MIGHT. Why? Well, the fan has a 4-pin connector on the end of its cable, so we would assume it actually is a PWM-type motor. Further, most CPU_FAN headers are set by default to use PWM Mode. BUT if the fan actually is only the older type (a 3-pin fan), that type of motor cannot have its speed controlled by this Mode. A 3-pin fan on a PWM Mode header will always run full speed which is what you describe. If that does not change its performance, switch it back to PWM Mode again.
Now you can try a test to detect whether your mobo actually can control this fan. Among the options for the CPU_FAN header, it is probably set to "Normal" or "Automatic" PROFILE - that is, to do automatic fan speed control. But I expect it has other options like running constantly at a high-performance (fiull speed), or at a Quite profile (constant slower speed that is quieter but gives LESS cooling), or maybe a Manual setting shich allows you to set your own speed choice. Try one of the forced lower-speed options and see whether that really does run the fan slower. If you CAN force the fan to run slower this way, then the control system CAN do speed control as needed. Now return it to the "Normal" or "Automatic" Profile so it uses its automatic speed control ability. If the fan still wants to run full speed, that indicates that it believes your CPU chip's internal temperature is quite high and it really needs that much cooling.