The issue at hand was being above the 3ish degree slope. I've yet to hit a mast, a tree or even a train station being above slope...
I'd personally be deliberately above slope on a PAPI or ILS in a piston single on a nice day and descending to it or well below depending on my desired taxiway.
If your instructor was setting the exercise on a single approach to test your aircraft handling then fine. If not then I think he has a case of shiny jet envy and is trying to fly a Cessna in the way of a Boeing as that's where he wants to be. He's doing himself and his student a disservice.
As ab aside the PAPIs are in many places set up fir A380 eye height. So if you are flying them to the ground (even in a A320) you'll land a looong way down the runway.