The plastic plate was vital to force air through
the power supply from the front to the back. By removing the plate you've short-circuited the path of air and now more than half the components in your PSU are getting barely any airflow - most of the airflow they receive will be recirculating eddies of hot, trapped air.
Now, without the plate, there's a dead spot under the front half of the fan because it's balancing against the backpressure from the other half of the fan. If you're thinking "no, the pressure is less there because the air escapes out of the vents at the back of the PSU" you'd be wrong; Fluid dynamics don't work that way. The fan creates pressure and the fact that air can escape just means that more air flows in the back half.
What you'll find is that a little bit more air flows out of the back of your PSU now, but it's likely to be cool air that hasn't actually passed over any components in your PSU - it's come in through the back half of the fan, met almost zero resistance and found a direct escape route out of exhaust vents. Given that there's now no airflow under the fan hub, and given where the heatsinks are in relation to the fan, I'd estimate that you've lost two thirds of your cooling now.
I hate to state the obvious, but if you don't understand something - especially when it involves high voltages, expensive hardware, shock or fire hazards - you really should do some basic research before assuming that the thing you don't understand can be tossed out. The engineer who engineers stuff for a living put that in there. What makes your guesswork better than his years of training and experience?
Failing that, resort to common sense; If the manufacturers could save $0.05 by omitting that plastic part and two screws on hundreds of thousands of PSUs, they'd do it in a heartbeat. It must be necessary even if you don't know why.