Except the case of Flint, where in the article I linked to, the people who set the threshold of 5 have had to backtrack, and reassure parents that their children are not really "poisoned". The article also mentions concern over the stigma those kids will carry going forward of being labelled as "brain damaged". Such labelling isn't cost-free, and can wreak serious emotional damage on parents and children.

But Edwards says that labeling children as “brain damaged” is also unjust. “Poisoning is obviously a loaded word,” he adds. “I’ve spoken to many parents in Flint, and I’m concerned because I don’t want children there defined by what happened to them

https://www.scientificamerican.com/article/flint-s-lead-tain...

You will notice all the caveats in the article above, that are generally ignored in mainstream reporting of scientific studies around lead.

If you can recommend a better strategy, I'd like to hear it.

How about scientific studies that actually attempt to quantify the effects of lead, to determine an actual threshold of harm, handle confounding properly, and avoiding emotive and alarmist tropes when publicizing the results of those studies?

Alarmism may be useful in the short term for getting action taken (and getting funding), but in the long-term, it will cause people to "tune out" or worse, to adopt anti-science attitudes (see current Global Warming skepticism).