I guess the risk some people are concerned about is the way blood is collected, or the consequence of knowing about a metabolic disorder, such as needing a special diet etc.
Most of the tests on the newborn screen can be accomplished without actually digesting or metabolizing, so you theoretically could send the screen on cord blood. Some would not be picked up. There are other ways to collect the blood, such as a venous draw that would not cause as much injury as a heel prick. The reason there are laws is people view it as a right of the individual child to have a life with full mental capacity, and finding out about metabolic disorders early and treating appropriately, will prevent the loss of cognitive abilities. The most concerning disorders are the ones picked up early if the test is done at 24 hrs from first meal to 2-3 days.
It seems there is some misconception about the treatment always being interruption of breastfeeding. Even with PKU disease some breastfeeding is acceptable as long as the levels are not too high. For a child with metabolic disorder, the byproducts of digesting food can act like poisons disturbing the normal function of the body and mind. Most of us would never poison our own children, if your kid has galactosemia or something similar, that is what allowing the disorder to go undiagnosed or treated would do.
To the OP, I guess many parents are having difficulty what problem you have with the newborn screens, most of them have been prompted by strong advocacy of parents who don't want other people to go through watching their children suffer needlessly.