The F-duct was a clever work around of the old F1 rule of no moveable aerodynamic devices (which dates from the 70's) and was motivated, intially by the practice of mounting the rear wing directly to unsprung parts of the suspension. A more applicable example of the rule was the late 70s brabham fan car which used a large fan at the rear (ostensibly for engine cooling purposes) to suck out air from the underside of the car to add downforce. Think of the hyperloop design, in reverse.
By making the only physical moving part in the f-duct design the driver (who obviously has to be allowed to move), the devices cleverly adhered to the letter of the law. The driver would close a hole in the cockpit which allowed some air to pass or not to a fluidic switch (think of a transistor), which would influence the flow of a larger stream of air to the rear wing).
One issue with banning the engine mapping that blew the diffuser off throttle was that this was already being done by many engine manufacturers for engine cooling purposes, and thus could not be easily regulated. Even their year end attempt at a fix by specifying the location, pointing direction, etc of the exhaust outlets didn't work (see coanda effect / downwash exhausts of 2012). They have finally addressed the solution in 2014 regulations by specifying that the exhaust outlet has to be behind all bodywork.
It's also worth pointing out that exhaust blown diffusers are more than a decade old, but in the past suffered from the problem of changing the balance of the car drastically mid throttle (when the driver gets on the throttle) due to 1) less advanced engine mapping), and 2) directly feeding into the diffuser venturis. In fact, for a long time, the standard solution (periscope exhausts pioneered by ferrari), sought to remove as much influence of exhaust air on the aerodynamics as possible to make the car's balance unaffected by engine exhaust volume, so given that environment, no one was worried about anyone using the exhaust for aerodynamic benefit. The modern (Red bull design) blown diffusers only channel a relatively small portion of exhaust air directly into the diffuser channel, and instead use a large portion of exhaust to blow over the top of the diffuser itself (enhancing the diffuser effect), and on the side of the diffuser (to provide a air skirt that prevents squirt air from the rear tires bleeding into the diffuser from the side which decreases efficiency), particularly on cars like the Red bull which run a high level of rake (which enhances aerodynamic downforce separately by placing the front wing closer to the ground but makes the diffuser more vulnerable to tire squirt and other effects).