Aphids

The farmers around here often grow carrots and I've never seen them netted. They do put massive swathes of enviromesh type stuff over young lettuces and spinach in spring, probably to shield them from bad weather and keep birds and animals off. There are systemic insecticides which they can treat seed with, so only the insects which feed on the young plants are harmed. They also use pyrethroids (like the stuff in fly killer aerosols) as sprays but they only kill the adult flies and don't control the larvae.