Interesting thread name,
"after tower gives surprise instruction", 
give me a break, this is a normal flight operation. If I, or anyone else here had been on final behind this lad and been given a go around, we probably would be screaming at ATC, one is a practice approach and two is a full stop, ATC did exactly the right thing IMO.
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As far as student capabilities, the flight instructor is directly responsible for the student, bottom line, that is where the buck stops.
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IMO it
IS the Local controllers control zone, he is directly responsible for the separation of IFR traffic and participating VFR traffic, traffic permitting.