I was amazed when I got to know that there is such a simple mechanism know as Trompe to compress air. It has no moving parts which make it cheap to construct and do not require any servicing. Even the air being compressed has negligible moisture and its operation makes less noise unlike the compressors used in industries. If this system has so many positive points so why it is not used widely? Is it due to its big size?
Simply because it's so wasteful regarding energy. If you employ the flow and height difference of water for a hydroelectric generator to power a standard compressor (be it piston, centrifugal, or just a big fan), you can achieve vastly better pressures and air flow than with a trompe.
Additionally you won't need to have the water drop and air intake in the same place, so instead of air ducts and aqueducts/trenches/pipelines you can use much more convenient electric cables to bring the energy from the source to where the air flow is needed. Which is rather important, especially for larger installations - in case of the trompe you're limited to vicinity of rivers and streams with large height difference over short distance, which are on themselves rather rare, and you can't transport the air thus produced very far.
The definite upside of the trompe is that it's very fail-proof. Where the location allows, and there is no need for a more efficient solution, it can do its work very well for long time with minimal maintenance - other than removal of foreign objects brought by the water flow, it hardly needs any servicing. But the limitations make such situations rare, plus if it's a significant installation, you're still better off producing hydroelectric energy and using funds obtained from surplus sold to maintain a good compressor.