The benefit To brining tomatoes to the compost is soil temp. Tomatoes need warm, they hate chill and one bad night in the low 40s can stunt your plants setting you back weeks, The biological breakdown or organic matter gives off heat, so the soil on your compost pile can be 10-15 degrees warmer that the rest of the yard. That's why it works so well, it's not the richness of the compost, it's the warmth.