Its more about the other way around. Reducing the airflow as little as possible by removing obstructions.
How much volume a fan can move is dependent on the RPM and the static air pressure between the front and back of the fan.
Here is an example chart for a random fan:
As you can see increasing the RPM increases the flow while increasing the static pressure reduces the flow. Static pressure is the difference in pressure between the front and back side of the fan. If you put a filter on the fan this causes resistance to air flow so the static pressure goes up until there is enough to push the given airflow trough the filter. The ideal case of 0 static pressure is typically where the CFM of a fan is specified (Fan hanging in free air with no obstruction). The other extreme case is blocking off the fan completely, this drops the airflow to zero but the fan will be producing the maximum air pressure it can. A realistic heatsink is somewhere in between like the filter from before.
This characteristic curve is dependent on the fan design. The shape of the fan shroud and shape of the fan blades can optimize a fan for more air flow or more static pressure at a given RPM. A office fan is optimized for flow as it doesn't need pressure while a jet engine compressor turbine is optimized for pressure as it needs to produce a lot of pressure rather than just flow.