The main reason for why blower heatsinks are used a lot in mining, is because of the stacking of the GPUs. Open-frame coolers perform better when they are separated by a considerable distance AND there is a continuous stream of case airflow to carry the warm air away from the GPU, so that the hot air isn't recycled by the open-frame fans.
Blowers work much better in tightly packed cases (multi-GPU setups or open-frame mining beds), because they circulate air in a linear path and don't recycle between two closely spaced GPUs. So you can stack more GPUs closer, with about 1 cm being all that is necessary. You can't do that with open-frame coolers under load, because they'll recycle hot air and overheat.
For mining, you want to use as little electricity as possible, and so people typically do open beds of mining GPUs. This allows the room to be cooled with just regular airflow. With open-frame coolers, this is harder, because you have to provide an external source of airflow to push the hot air away from the GPUs, because the flow path is not linear. That costs more money and if not done properly, can cook GPUs prematurely and then your profit evaporates.