Traveling at 800-850+ Km/Hr the supposed screen have to be very strong to withstand a 3kg bird strike. Make them light and the strike may take with it parts of the metallic/composite material of the screen along with the bird into the engine, multiplying the problem rather than resolving them. Make them strong enough to withstand that kind of force and they will be too heavy.
Then there is the issue of turbulence in air entering the engine.
Also a mesh at 35000ft appx will be subjected to -50 Celsius temperature and the mesh will act as a suitable surface for icing. Now you may have a bird strike every now and then but icing is a regular thing on all flights. The chunks of ice breaking from the mesh and entering the engine will again create more problems than it resolves.
In last 50 years or so there have been two or three serious bird strike accidents on commercial flights. Just not worth it keeping in view all the above mentioned regular troubles!