Which allows the mass to trasfer from the chopper to the enviornment. If the plate was attached then the reaction of air on the plate cancels the reaction of the air leaving the blades, just as an astronaut in space throwing a rock at his feet, if he hits his foot he doesn't move, if he misses then he will move the opposite direcetion as the rock. Your example only proves this point.

BTW the air pressure above the blades will be lower than the air under it, so both work, they just use differant ways to come up with the same answer.