As far as I know, the plastic engine covers serve a few minor purposes:
1) For looks - They clean up the look of the engine bay (sorta). Modern engines have so many more wires than older vehicles. It is hard to get that clean open engine bay like you find in some muscle cars. Instead of taking painstaking effort to make every wire look appealing, they cover it all with plastic now.
2) For cleanliness - They keep dust/dirt and water from getting near wires, connectors, sensors, cables, and/or moving parts.
I don't think taking the cover off would hurt anything, but IMO you would have to clean up the wiring and other parts to make it look good.
the two primary purposes from an engineering standpoint are heat and noise reduction. The esthetics of a clean engine bay is just a bonus