QFE or QNH both make some sort of sense - either Oft or the airfield elevation on touchdown. QNE gives you reference to neither very well and is a pointless throwback to the era of limited mechanical altimeters.
I suppose it makes sense if you are still operating really antique equipment AND operating out of Bogota. QFE makes more sense for a largely UK based operator but makes little sense to a largely worldwide operator. If the likes of BA and Virgin and the rest of the airline world use QNH it is not for a whim. Terrain awareness and IAS/TAS issues at hot and high airfields tend to push you towards QNH for safety reasons. QFE is fine for a parochial, inwards looking, UK centric operation.