Tomato roots need warmth above 70 degrees in ground temperature to grow. Below that temp they just sit. Therefore plastic speeds up the growth and keeps it going into the night. It takes a large number of leaves, about 14, to support the sugar production needed to produce one fruit. Pinch suckers and leaves and you pinch the future fruit.
Tomatoes are cousins to nightshade and have poisonous leaves, but edible fruit.
The leaves may cause an allergic reaction in some folks. It seems like a lot of work, but in reality it is mostly in preparation and planting. The plastic keeps the weeds down and moisture in so all you have to watch is that they are watered and that the hornworms don't get to them.