I’ve read all the books, I’ve played the games—there is nothing in either medium to suggest that prop are not still in use. Do you know why the modern military uses jets for most military aircraft? Because they have to accelerate to high speeds. Do you know why they still use props in drones and helicopters? It’s because they have to hover.
It’s really a simple matter, as a jet aircraft accelerates it thrust grows accordingly. A prop produces constant thrust, they actually measure it in horse power, and it relates directly to atmospheric pressure—an aircraft using only prop power cannot break the sound barrier or fly at very high altitudes. This is not the case in a jet engine, the heated air, the pressure produced by the burning of fuel, between the turbine fans in a jet is of a much greater pressure than the atmospheric pressure, so the air inside the jet can move much faster than air at normal atmospheric pressure. As a jet aircraft’s speed increases it actually becomes more efficient because it can pressurize even more air and produce faster exhaust velocities. However, there are three conditions that limit this. The shape drag coefficient of the intake and the amount of air it can intake will result in diminishing returns eventually, or the drag increases in the combustion chamber (an aircraft cannot travel past a certain speed if its engines cannot produce thrust traveling faster than that speed), or the engine melts itself due to super heated gases. This also explains why a prop engine plane can take off from a much shorter runway than a jet plane, they also can take off and hover using far less fuel.
So….while a jet engine makes perfect sense for a vehicle that has to travel very fast, or at high altitudes, it makes no sense for a vehicle that needs to hover to provide close air support.
There is also seems to be a mistaken notion that a prop is somehow more vulnerable to damage than a jet engine. This couldn’t be further from the truth, particularly in the case of the fans in the original picture. Note that the fan blades are enclosed, this is the primary danger of a prop—flying low its edge hits a tree or cable and snaps, but that wouldn’t happen with it enclosed like that. The only advantage that a jet might have is it is a small target area, however it still uses fan blades to build up internal pressure—moreover, it’s filled with pressurized fuel. A jet engine is just a controlled explosion; a bullet that penetrates the side or front of a jet engine will probably severely damage it, hell, small birds and rocks frequently severely damage military and commercial airliner's turbofan engines—modern props can handle impacts much better. In fact, in a multi bladed prop, a blade can shatter and if the damage is low enough, you can run it at lower RPMs and the prop can maintain some of its integrity and efficiency (particularly the newer props). In a jet this would cause a massive cascade of damage (there are between 10-20 fans in most jet engine, if one blade is destroyed its shards have the potential to cause a domino effect to the very hot, and thus fragile, exhaust fans). There are special ducting systems in jets designed to take off from rugged terrain, but they significantly decrease their efficiency.
The Sparrowhawk has the best of both worlds. Jet’s for fast forward motion and fans for hovering for long periods of time.