Why do No Tail Rotor (NOTAR) helicopters use an enclosed variable pitch fan? Aerotécnica AC-14 was an early no tail rotor prototype which used the ducted exhaust from the turboshaft to counter the torque of the main rotor. The concept seems simple with few moving parts. 

It didn't use a (seemingly complicated) enclosed variable pitch fan driven by the main rotor transmission, neither did it use Coandă effect (even if it may have), like modern NOTAR does.

Why has a much more complicated solution been adopted for modern no tail rotor systems, and why was AC-14 concept abandoned?

(Autorotation yaw behavior may be one safety issue, even if autogyro autorotation procedures are quite safe.)
They use a shrouded fan because these use less power than a jet for generating the same thrust. I could find a reference in Principles of Helicopter Aerodynamics by J. Gordon Leishman: he states that using jet exhaust for anti-torque required high power and that directional sensitivity was poor. 


Hiller Aircraft made a tailless prototype. 
The Nord Norelfe was constructed in 1954 and was used for the Aerotecnica AC-14 mentioned in the OP. 
The design was tested in the Cierva-Weir W-9




The reference to high power would refer to the generic issue with jets providing thrust: it costs less power to accelerate a higher volume of air to a lowish velocity (like a propeller does) than to accelerate a lowish volume of air to a higher velocity (like a jet exhaust does).