Nick, I gave this a few moments of serious thought and concluded that there's just no way you could make anything which would "retract into the cowl" and be strong enough to do any good (has to withstand the force of a body walking into it aided by the airflow from the prop) without making the cowling at least twice as big as it is and adding at least a hundred pounds or two. Just moving something from the front of the prop to behind it without risking contact with the prop (and associated costly damage) would require something pretty fancy. And given the market for such a device, you'd probably be talking of around $200,000 installed.
There's much talk about how to make flying cheaper. Suggesting cages for props takes things the other way, big time. If the government decided to mandate cages, we might as well give up flying. The weight, complexity and resultant cost would ruin the airplane and it would never sell. And its prop would therefore never kill anyone, either. Mission accomplished.
Jets don't use screens because of the drag and the problem of ice accumulation. The ice would either choke off the airflow, or break off and go into the engine and bust things. Heating that screen would cost a huge part of the engine's power. It already costs plenty to heat the inlet lip and fan hub.
Small ducted fans, of the size we'd use with piston engines, have seldom worked well at all. Too much drag, and losses associated with small diameters and high RPMs. On turbofans they are large, and the duct is to slow the incoming air to increase its pressure. That isn't necessary on a small piston-powered fan.
It comes down to one thing:
Don't Be Stupid. Don't let the uninformed near running airplanes. Don't let dogs or kids run loose around airplanes. Never board or deplane people with the engine running. Don't hand-prop unless you know the hazards and have some training.
What's next? Cages under the lawnmower blade to keep guys from running over their feet or sticking their hands underneath to clear the clogged grass? Electronic finger detectors and superfast brakes for skilsaws? A cancer vaccine added to every cigarette?
Dan