Why air compressing mechanism "Trompe" is not popular in usage?

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.