Trouble with your instructor's scenario (if he's saying his way is the only way) is that it's so specific - what if the thrust was stuck at 90% or 40% for example?
Two points to ponder - if you leave it running, do you plan for a flap 15 landing and use the QRH checklist for this - GPWS warnings with thrust lever asymmetry on the approach spring to mind. And what go-around flap setting will you use with thrust available less than normal two engined go-around?
And the big one - landing. If you leave it running, the flare's gonna be mighty interesting as you cruise along in ground effect with 77% N1 on one side, and large, changing rudder inputs being suddenly needed so close to the ground. And if you decide that the co-pilot will shut it down in the flare, all the normal cross-checking has gone out the window - it'll be very interesting in this rushed situation if he/she shuts down the wrong one.
Then, once on the ground, if you've decided to leave it running until the landing roll, things will get very interesting again as you're stuck between running out of runway or falling below Vmcg before it's shut down. And as Anthony Carn has already said, thrust reverser won't work.
Being devil's advocate to some extent, as unusual situations like this must be evaluated on the day, but I definitely prefer the relative predictability of a shutdown. The shutdown has you working within the SOP's - the other way, you're out there on your own.