I would also be very troubled of the possibility that mass testing in children would, itself, cause some degree of anxiety. I know I don't enjoy being tested.
My point is that taking a physical does not change your physical attributes; being asked "are you nervous?" can't give a proper answer because the question, by itself, changes the outcome. Like the "whatever you do, don't think of a pink elephant" thing.
I'd assume that a mental health screening would be designed to work with children and their caretakers to avoid these scenarios. In any case, this is only an argument for the lower half of kids. They're starting at 8 years old. They aren't toddlers.
If there are enough troubling signs, you look into it a little more. It might be nothing, it might be something to work on.
