As a player who just played his first tournament in the Rec division. Yes, I want a trophy. I could care less for a stack of plastic. I have a stack of plastic at home. A trophy of some sorts would give me pride. Whether it be a small gold-painted plastic figurine on top of a sparkly blue pole attached to a fake marble base or a custom dyed "Rec Division Champ" disc, a trophy would be a thousand times cooler than a Champ Destroyer that everyone else carries.
As far as Intermediate and Advanced divisions go, you may be looking at a different beast.
Some sort of tiered reward system I think is required (from the PDGA) in the amateur divisions to promote advancement in skill and deter sandbagging. This might be a good start.