It is better to have a quiet fan that meets all of the requirements without any extra circuitry that can fail. You can make a fan more quiet by adding a series resistor. Experiment to find the right value, but perhaps start with around 500 – 1000 ohms.
Another easy solution is to simply run the fan from the 12V transmit power, assuming that is not what you are already doing. No reason to run the fan while receiving.
If a noisy fan is the only choice, then putting in a controller to minimize the noise while still removing the heat is the next best solution. If properly designed, installed, and tuned, then there would not be a change in the amount of heat that can be removed as the heat sinks get hotter. The response time can get in the way of keeping the finals cool quick enough to not cause an issue. An always on at max fan does not have this issue.
Woody KZ4AK suggests fan controllers are easy to build and minimize noise when not needed.
Something like these… YMMV
Variable analog – Had to add the 3.3 ohm to reduce induced noise in the uBITx from high current fan.
OR
Switched – OFF/ON
Inexpensive fans can be had surplus, like at:
https://www.allelectronics.com/category/220/fans/1.html
https://www.mpja.com/DC-Axial-Fans/products/48/