There are twothree problems with this idea:
(1) To make a screen strong enough to withstand the body of a 15-to-20 pound bird hitting it at 500 miles per hour, would require thick wire which would significantly block air flow.
(2) Such a screen would be very liable to collect ice, so it would have to be heated to high temperature. This would be expensive and would increase the maintenance burden for the aircraft.
(3) If part of the screen failed and broke off for any reason and went into the rotors, it would destroy the engine.