Oh my god! He restarted it, and took off without warming it up!
. Fool.
The only fixed pitch propeller I have ever stopped in flight is that of the C 150 I own. I consider doing this on the verge of abusive to the engine if not done very gently, and I would not do it to someone else's airplane without good cause. Fooling around is not good cause. And, if you got things wrong at the end, and damaged the plane for lack of power, it would be hard to explain.
I am required to [stop engines] and feather propellers during flight testing on twins (usually the left), and then do a number of maneuvers. This can involve both a windmilling or feathered propeller, depending upon what is being done. I'm always happy to do this work on a PT-6 powered aircraft, where I can feather the prop without stopping the engine.
Piston engines can be grumpy when restarting in these conditions. If you cannot unfeather and windmill start, a starter start of a feathered prop will usually shake the engine a lot, and if not handled well could result in an overspeed. I always allow an extra thousand feet or so to continue a descent if needed, while the restarted engine is warmed up gradually, and its ability to deliver power smoothly is confirmed.
During twin training I was trained to shut down and restart in flight, though I agree with Big Pistons, that it is not a necessary enough exercise for a new pilot, to warrant the risk and possible harm to the engine.