My instructors tend to pull the throttle at about 200-300 ft to see how I react, then when they say "OK" then I can push it back in and keep climbing
A dangerous technique and proves nothing. By closing the throttle at 200 feet hardly has the student lowered the nose when he has to go around again. If the engine fails to pick up when the throttle is opened again then there is no time for the instructor to recover the situation in terms of field selection. What sort of weird instruction is that?
Far better to wait until a higher more suitable altitude where there is sufficient time for not only the student to select a suitable forced landing field but also to conduct essential safety checks depending on the aircraft type. It also gives the instructor sufficient time to evaluate the students actions so that a meaningful assessment of his skills can be made. And it also gives a fighting chance of regaining power if the engine fails to pick up during throttle opening. Throttle linkages have been known to break with jerky or rough handling by the instructor or student - especially when rapidly closing or opening the throttle as in simulated engine failure. Good threat and error management would dictate a safe altitude before closing a throttle in a single engine aircraft to simulate engine failure.
Think about this one on a similar subject:
It is common for some instructors to cut the mixture control in a twin to simulate engine failure after take off. They claim this is more realistic than using a closed throttle. They conveniently disregard the risk involved with a mixture cut that the engine may not restart and thus the pilot is left with a windmilling prop at low airspeed and altitude.
Yet, ask anyone why not cut the mixture on a single engine aircraft (rather than the throttle closure) to simulate an engine failure after take off?
Their answer would be unprintable, but generally it would be obvious there is a perceived danger of the engine not starting when mixture was re-introduced. Yet pilots are still happy to risk a failed start on a twin following a mixture cut simulated engine failure. Strange logic?