The problem with E is that it is a bit too strong. Does the author assume that a child resides in every single home that has lead paint? No, she doesn't need to make this assumption. She is only taking for granted that children live in some of those houses, not all of them.
The real problem is the word "eradication." There is no evidence to say that lead poisoning has been eradicated anywhere. It has only "declined steadily since the 1970s." It is certainly possible that there are lead sources other than house paint. This is why C is correct. If the author had argued that lead poisoning would decline in the area, that would make more sense.