Then, instructors placed great accent on the safe recovery from bounced landings and demonstrated the technique of applying a little power
Clare prop.
See above from the OP.
So why add power ie MORE energy to the situation unless it is to go around?
I think a little common sense needs to be applied here. Perhaps this extract from the current Boeing 737 Flight Crew Training Manual might help you understand things better: It applies equally to light aircraft.
"Bounced landing recovery - if the airplane should bounce, hold or re-establish a normal landing attitude and
add thrust as necessary to control the rate of descent. Thrust need not be added for a shallow bounce or skip. When a hard high bounce occurs, initiate a go-around."