Tartare, if you look at propulsion theory, you get maximum efficiency by accelerating an infinite amount of air an infinitesimally small amount. Pure jets accelerated a small amount of air a huge amount - turbofans accelerate a much larger amount of air a smaller amount and hence are way more efficient. That's the reason for the ever increasing bypass ratios of the turbofan engines. Problem is as the fan gets bigger, the weight of the inlet, fan duct, containment ring, drag of the cowling, etc. tend to cancel out the improved propulsion efficiency.
A turboprop or unducted fan gets rid of all that weight and drag, but creates other problems. Of course there is the noise (especially with counter-rotating props which is pretty much a worst case for noise) and blade out. But efficiency wise, having an inlet provides a huge advantage for high-speed flight. With an inlet, the speed of the air at the fan face is pretty much independent of the flight speed - the engine fan doesn't see much difference between takeoff and Mach 0.8 cruise. Hence you can keep the fan speeds sub-sonic most of the time even at high speed cruise (good for efficiency) where as unducted props go supersonic at high speed cruise (very bad for efficiency). The newer prop designs have moved that cruise speed at which they go supersonic quite a bit higher, but still well short of ducted fans.